leanified/CoreReader/Adopted.lean

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Philosophy 0.2.1 · considered Core 0.1.2. This view uses the repository’s public target catalog, readers and Lean files. Presentation does not change their judgments.

Expand Lean and line explanations · 1225 lines

LeanLine explanation

L1import CoreReader.Integration

Import the checked Logic, Evidence, Choice and Agency examples through Integration.

L3namespace CoreReader.Adopted

Place the following declarations in CoreReader.Adopted.

L4open CoreReader.Logic CoreReader.Agency CoreReader.Evidence CoreReader.Choice

Make the four helper namespaces available without qualification.

L6/- These are three explicit mathematical assessment tasks, not an exhaustive or

The comment limits the encoding to three explicit mathematical task forms.

L7exclusive taxonomy of claim natures. A task fixes the original claim and support

These forms are not an exhaustive or exclusive taxonomy; original claims and support must be fixed.

L8context before any candidate assessment is proposed. Its identity must be retained

The support context is fixed before proposing a candidate assessment.

L9when comparing alternative assessments; taskOfFacet declares a new task and does

Alternative assessments must retain task identity; taskOfFacet instead declares a new task.

L10not authorize replacing a previously identified task. -/

Declaring a new task does not authorize replacing an existing one.

L11inductive AssessmentTask (W : Type) where

Define task data over an arbitrary world type W; constructing data proves no fulfillment.

L12  | empirical (records : List (Record W)) (scope claim uncertainty : Claim W)

An empirical task stores the original records, scope, claim and uncertainty predicate.

L13  | inferential (assumptions : Theory W) (claim : Claim W)

An inferential task stores the original assumptions and conclusion.

L14  | value (position : ValuePosition W)

A value task stores the complete position, including its reasons, limits and consequences.

L16def taskOfFacet {W : Type} : Facet W → AssessmentTask W

Convert a facet into the new assessment task it itself declares.

L17  | .empirical records scope claim uncertainty => .empirical records scope claim uncertainty

Copy every empirical field into the newly declared task.

L18  | .inferential assumptions claim => .inferential assumptions claim

Copy the inference's assumptions and conclusion without adding support.

L19  | .value position => .value position

Preserve the complete value position in the new task.

L21/- This is a content-based sufficient adapter for the declared task, not a

Describe a content-based sufficient adapter for a declared task.

L22philosophical rule requiring one unique assessment form. The empirical task may

This finite adapter is not a philosophical demand for one unique assessment form.

L23also be assessed inferentially from exactly its observation/scope premises; its

An empirical task may use inference based on exactly its original observation and scope premises.

L24original uncertainty obligation is still checked. In particular, adding the

Changing assessment form still retains the original uncertainty duty.

L25conclusion as a new premise cannot replace the original empirical grounds.

Assuming the desired conclusion cannot replace the original empirical grounds.

L26The finite adapter need not accept every semantically equivalent presentation. -/

The finite adapter does not promise to accept every equivalent presentation.

L27def NatureAppropriate {W : Type} : AssessmentTask W → Facet W → Prop

Define appropriateness as a relation between an independently fixed task and a candidate facet.

L28  | .empirical records scope claim uncertainty, .empirical actualRecords actualScope conclusion actualUncertainty =>

Compare an original empirical task with a candidate empirical assessment.

L29      actualRecords = records ∧ actualScope = scope ∧ conclusion = claim ∧ actualUncertainty = uncertainty

Require exact equality of records, scope, conclusion and uncertainty content.

L30  | .empirical records scope claim uncertainty, .inferential assumptions conclusion =>

Handle an inference proposed for the same original empirical task.

L31      assumptions = singleton (fun w => Compatible records w ∧ scope w) ∧

Require its assumptions to be exactly original record compatibility together with original scope.

L32      conclusion = claim ∧ Supports records uncertainty

Retain the original conclusion and require the original records to support the original uncertainty predicate.

L33  | .inferential assumptions claim, .inferential actualAssumptions conclusion =>

Compare original and candidate inferential tasks.

L34      actualAssumptions = assumptions ∧ conclusion = claim

Require the same assumptions and conclusion; a new conclusion-assumption is not admitted.

L35  | .value position, .value actualPosition => actualPosition = position

For a value task require equality of the entire position, not just its selected option.

L36  | _, _ => False

Reject all other task/facet pairings in this disclosed finite adapter.

L38theorem taskOfFacetAppropriate {W : Type} (f : Facet W) : NatureAppropriate (taskOfFacet f) f := by

Prove that a facet matches the new task declared from itself; this says nothing about another original task.

L39  cases f with

Split the proof over the three facet constructors.

L40  | empirical _ _ _ _ => exact ⟨rfl, rfl, rfl, rfl⟩

The empirical case supplies four reflexive content equalities.

L41  | inferential _ _ => exact ⟨rfl, rfl⟩

The inferential case supplies reflexive assumption and conclusion equalities.

L42  | value _ => rfl

The value case uses reflexive equality of the complete position.

L44/- Core 0.1.2 requires appropriateness to the original claim task. Supplied facets

Explain that the adopted Core 0.1.2 task needs appropriate assessment.

L45are an explicit assessment scope, without importing Core 0.1.3's all-applicable

The supplied facet list is the explicit represented scope of assessment.

L46coverage requirement. No claim-kind label or freely assigned success flag proves

No Core 0.1.3 all-applicable coverage rule or self-validating kind label is introduced.

L47appropriateness: NatureAppropriate compares the actual task and facet contents. -/

Appropriateness depends on actual task and facet contents.

L48/-- organon-map CoreReader.Adopted.Grounds012

Begin source-tracing metadata for CoreReader.Adopted.Grounds012; this mapping is not a proof premise.

L49organon.grounds#p1 sha256 4ee74dc8617388ee75d63b507176ecb73b8527758b648f7c588d3ae7f3445ec6

Record source clause organon.grounds#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L50organon.grounds.assessment#p1 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L51organon.grounds.assessment#p2 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L52organon.grounds.assessment#p3 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L53-/

Close the preceding source-mapping comment without adding a logical condition.

L54def Grounds012 {W : Type} (claim : Claim W)

Define Grounds012 for an explicit claim over W.

L55    (articulations : Facet W → Articulation W) (facets : List (Facet W))

Parameterize it by the actual articulation function and proposed facet list.

L56    (task : AssessmentTask W) : Prop :=

Also require the independently fixed original task as an explicit parameter.

L57  facets ≠ [] ∧ ∀ facet ∈ facets,

Require a nonempty list and examine every listed facet.

L58    facet.claim = claim ∧ Articulated (articulations facet) ∧

Bind each facet to the same claim and require identifiable articulation.

L59    FacetArticulated (articulations facet) facet ∧ FacetDischarged facet ∧

Require articulation to match the facet's contents and require its represented assessment to be discharged.

L60    NatureAppropriate task facet

Also require appropriateness to the original task; same conclusion alone is insufficient.

L62/- This helper proves the newly declared taskOfFacet f only. It supplies no

The helper's conclusion concerns only its newly declared taskOfFacet f.

L63appropriateness proof for another, previously fixed task with the same claim. -/

It cannot supply appropriateness to a different existing task sharing the conclusion.

L64theorem grounds012Singleton {W : Type} (f : Facet W) (h : FacetDischarged f) :

Assume the supplied facet f is already discharged; the helper does not prove that premise.

L65    Grounds012 f.claim canonicalArticulation [f] (taskOfFacet f) := by

Conclude Grounds for its canonical articulation and its own newly declared task.

L66  refine ⟨by simp, ?_⟩

Prove the singleton list nonempty, leaving its universal facet obligation.

L67  intro facet hf

Introduce an arbitrary listed facet and its membership proof.

L68  cases List.mem_singleton.mp hf

Singleton membership identifies that facet with f.

L69  exact ⟨rfl, canonicalArticulated f h, canonicalFacetArticulated f, h, taskOfFacetAppropriate f⟩

Combine claim identity, canonical articulation, the assumed discharge h, and task-content identity.

L71/-- organon-map CoreReader.Adopted.generationSpecification

Begin source-tracing metadata for CoreReader.Adopted.generationSpecification; this mapping is not a proof premise.

L72organon.charter.overview#p2 sha256 75d7d941d3c07ea748c4a9261d36a75fbd5664ff9c817c4034a9a36a3a12664c

Record source clause organon.charter.overview#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L73organon.charter.overview#p3 sha256 75d7d941d3c07ea748c4a9261d36a75fbd5664ff9c817c4034a9a36a3a12664c

Record source clause organon.charter.overview#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L74organon.charter.self-transcendence#p1 sha256 f4ca590e2ae15e3882f70c7b2bc46a8911c97cee547c8b137b5493fbf862c8c0

Record source clause organon.charter.self-transcendence#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L75organon.charter.self-transcendence.orientation#p1 sha256 7f9b85c0816b3d69e417cf3cbe17b7b59931388f84d799ce6730c998037358bf

Record source clause organon.charter.self-transcendence.orientation#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L76organon.charter.self-transcendence.non-finality#p1 sha256 4ae4497523e79e0606ab3849c47b6ea16f8888a952e063e6966eb36b750f3df8

Record source clause organon.charter.self-transcendence.non-finality#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L77organon.charter.self-transcendence.limits#p2 sha256 6dade83f0b7fcc004bdb37b6726c15b31b06a377de4e86d506c9d2e67847029d

Record source clause organon.charter.self-transcendence.limits#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L78organon.relationships.terms#p1 sha256 61cb7ce4f2920f1aa6771502b87a66536ae0504acccfebd9dd23bcc62756eddf

Record source clause organon.relationships.terms#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L79-/

Close the preceding source-mapping comment without adding a logical condition.

L80def generationSpecification (policy : Policy) : Prop := Generative policy

Generation satisfaction means valuing expansion and keeping every current form revisable.

L82/- All consequences use the whole currently held set. Historical reporting is

The consistency comment concerns joint consequences of the whole currently held set.

L83separate and does not require simultaneous compatibility with withdrawn claims. -/

Reporting historical change is separate from retaining withdrawn claims simultaneously.

L84/-- organon-map CoreReader.Adopted.consistencySpecification

Begin source-tracing metadata for CoreReader.Adopted.consistencySpecification; this mapping is not a proof premise.

L85organon.charter.consistency#p1 sha256 c6960c590c096d33250599cf418e3c6a1dc26bfc7d7800c82b8efde656950f42

Record source clause organon.charter.consistency#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L86organon.charter.consistency.meaning#p1 sha256 81c09e38a3349499f95401d1c08f6069666c13547a43bc4e4395330743055faa

Record source clause organon.charter.consistency.meaning#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L87organon.charter.consistency.meaning#p2 sha256 81c09e38a3349499f95401d1c08f6069666c13547a43bc4e4395330743055faa

Record source clause organon.charter.consistency.meaning#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L88organon.charter.consistency.limits#p1 sha256 4fa1c29bf95ad6ef04c6d27671a832c0af8ba31b9c0d8018a8d09c4f33c38e75

Record source clause organon.charter.consistency.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L89-/

Close the preceding source-mapping comment without adding a logical condition.

L90def consistencySpecification {W Q : Type} (before after : Snapshot W Q)

Define consistency and reporting for before/after snapshots over worlds and questions.

L91    (reported : Bool) : Prop :=

The Boolean report records whether a change was acknowledged.

L92  Consistent after.held after.context ∧ TruthfulReport before after reported

Require the current whole theory to be consistent and the transition report truthful.

L94/- A method's actual input and interpretation are parameters, permitting domain

The reflexive-rule comment allows domain-specific input and interpretation types.

L95methods as well as the small arithmetic adapter. Key coherence prevents records

The rule key must coherently identify one method.

L96for another method from silently satisfying the duty. -/

Work for another method cannot silently discharge this rule's duty.

L97structure ReflexiveRule (T I O : Type) where

Package a reflexive rule over targets T, inputs I and outcomes O.

L98  key : PrincipleKey

Store the rule's owner/local principle identity.

L99  activity : Activity

Store whether the rule concerns generation or assessment.

L100  applicable : T → Prop

Store the condition under which the rule applies to each target.

L101  input : T → I

Specify the actual input for each target.

L102  meaning : I → O → Prop

Specify which outcomes follow the method's meaning for each input.

L104/-- organon-map CoreReader.Adopted.reflexivitySpecification

Begin source-tracing metadata for CoreReader.Adopted.reflexivitySpecification; this mapping is not a proof premise.

L105organon.charter.reflexivity#p1 sha256 13293b45c2fa89068c68ae7ef3c5df38f0efadb3ef3873d78a5ba67d9691a757

Record source clause organon.charter.reflexivity#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L106organon.charter.reflexivity.meaning#p1 sha256 8a2caede01a43d8b6c60b54c78ac089c51868e9956f316948077ccee2e45c9cc

Record source clause organon.charter.reflexivity.meaning#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L107organon.charter.reflexivity.limits#p1 sha256 ac0baae0d86e69f84c1ca4dee837de2759e2d29c295ffc257d988962158d4bbc

Record source clause organon.charter.reflexivity.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L108organon.relationships.roles#p3 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L109-/

Close the preceding source-mapping comment without adding a logical condition.

L110def reflexivitySpecification {T I O : Type} (rules : List (ReflexiveRule T I O))

Define the obligation over a supplied list of generic reflexive rules.

L111    (isSelf : T → Prop) (performed : PrincipleKey → T → I → O → Prop) : Prop :=

Supply self-target identification and an actual performed-work relation indexed by key, target, input and result.

L112  (∀ p ∈ rules, ∀ q ∈ rules, p.key = q.key → p = q) ∧

Equal keys among registered rules must identify equal complete rules.

L113  ∀ rule ∈ rules, ∀ target, isSelf target → rule.applicable target →

For every listed rule and self-target, retain that rule's actual applicability condition.

L114    ∃ outcome, performed rule.key target (rule.input target) outcome ∧

Require an actual result performed on precisely that target and its prescribed input.

L115      rule.meaning (rule.input target) outcome

Require the same result to satisfy the rule's meaning relation.

L117def legacyRule (p : Principle) : ReflexiveRule Subject Inquiry WorkOutcome :=

Adapt an existing concrete principle to the generic reflexive interface.

L118  ⟨p.key, p.activity, p.applicable, p.inquiry,

Preserve its key, activity, applicability and inquiry function.

L119    fun inquiry outcome => p.meaning inquiry (p.reasons inquiry.target) (p.limits inquiry.target) outcome⟩

Evaluate meaning using the reasons and limits attached to this inquiry's actual target.

L121def legacyPerformed (rules : List Principle) (records : List WorkRecord)

Define the concrete work relation over existing rules and records.

L122    (key : PrincipleKey) (target : Subject) (input : Inquiry) (outcome : WorkOutcome) : Prop :=

Identify the exact key, target, inquiry and outcome being requested.

L123  ∃ p ∈ rules, ∃ record ∈ records,

Require a registered principle and an actual record in the supplied lists.

L124    p.key = key ∧ ValidApplication rules p target record ∧

Require the matching key and the contentful ValidApplication predicate.

L125    record.inquiry = input ∧ record.outcome = outcome

Bind the record's inquiry and outcome to the requested ones.

L127theorem legacyReflexivity (owner : Nat) (rules : List Principle) (records : List WorkRecord)

State a conditional bridge from existing concrete reflexivity to the generic interface.

L128    (h : Reflexive owner rules records) :

Assume concrete Reflexive satisfaction h; this is not established merely by the interface.

L129    reflexivitySpecification (rules.map legacyRule) (fun s => s.owner = owner)

The conclusion maps all original rules and preserves the owner's self-target predicate.

L130      (legacyPerformed rules records) := by

Use actual original records through legacyPerformed; begin the proof.

L131  constructor

Separate registry coherence from the per-target work obligation.

L132  · intro p hp q hq he

Take two mapped rules with memberships and an equal-key premise.

L133    obtain ⟨a, ha, rfl⟩ := List.mem_map.mp hp

Recover the first original rule a from its mapped membership.

L134    obtain ⟨b, hb, rfl⟩ := List.mem_map.mp hq

Recover the second original rule b likewise.

L135    exact congrArg legacyRule (h.1 a ha b hb he)

Use original registry coherence to identify a and b, then map that equality.

L136  · intro rule hr target ht happ

Introduce a listed rule, its self-target and its actual applicability proof.

L137    obtain ⟨p, hp, rfl⟩ := List.mem_map.mp hr

Recover the original principle underlying the mapped rule.

L138    obtain ⟨record, hm, hv⟩ := h.2 p hp target ht happ

Apply assumed concrete reflexivity h to obtain a recorded valid application at this target.

L139    refine ⟨record.outcome, ⟨p, hp, record, hm, rfl, hv, hv.inquiryIdentity, rfl⟩, ?_⟩

Choose that record's outcome and preserve its key, membership and inquiry identity.

L140    change p.meaning (p.inquiry target) (p.reasons (p.inquiry target).target)

Expose the original principle's meaning on its own inquiry and target-specific reasons.

L141      (p.limits (p.inquiry target).target) record.outcome

Retain the limits of that same target and this record's outcome.

L142    have ti : (p.inquiry target).target = target := hv.inquiryIdentity ▸ hv.inquiryTarget

Derive that the inquiry's embedded target is the target actually being assessed.

L143    rw [ti]

Rewrite the embedded target using that identity.

L144    rw [← hv.inquiryIdentity, ← hv.reasonsIdentity, ← hv.limitsIdentity]

Rewrite inquiry, reasons and limits back to the exact recorded fields.

L145    exact hv.followsMeaning

Finish with the record's already supplied followsMeaning proof.

L147/- These are fulfillment interfaces for the named mathematical adapters, not

The specification comment limits fulfillment to the named mathematical adapters.

L148universal empirical adequacy claims or definitions of all possible claim kinds. -/

It asserts neither universal empirical adequacy nor a complete taxonomy.

L149/-- organon-map CoreReader.Adopted.empiricalSpecification

Begin source-tracing metadata for CoreReader.Adopted.empiricalSpecification; this mapping is not a proof premise.

L150organon.grounds.assessment#p2 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L151-/

Close the preceding source-mapping comment without adding a logical condition.

L152def empiricalSpecification {W : Type} (records : List (Record W))

Define the empirical obligation with explicit original observations.

L153    (scope claim uncertainty : Claim W) : Prop :=

Keep its scope, asserted claim and uncertainty predicate as separate inputs.

L154  Grounds012 claim canonicalArticulation [.empirical records scope claim uncertainty]

Require canonical Grounds for the given empirical candidate facet.

L155    (.empirical records scope claim uncertainty)

Fix the original task to these same records, scope, claim and uncertainty.

L157/-- organon-map CoreReader.Adopted.inferentialSpecification

Begin source-tracing metadata for CoreReader.Adopted.inferentialSpecification; this mapping is not a proof premise.

L158organon.grounds.assessment#p2 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L159organon.relationships.roles#p2 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L160-/

Close the preceding source-mapping comment without adding a logical condition.

L161def inferentialSpecification {W : Type} (assumptions : Theory W) (claim : Claim W) : Prop :=

Define inference satisfaction relative to explicit original assumptions and claim.

L162  Grounds012 claim canonicalArticulation [.inferential assumptions claim] (.inferential assumptions claim)

Require the inference facet to fulfill the task with those same original assumptions.

L164/-- organon-map CoreReader.Adopted.valueSpecification

Begin source-tracing metadata for CoreReader.Adopted.valueSpecification; this mapping is not a proof premise.

L165organon.grounds.assessment#p2 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L166organon.grounds.assessment#p3 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L167-/

Close the preceding source-mapping comment without adding a logical condition.

L168def valueSpecification {W : Type} (position : ValuePosition W) : Prop :=

Define value satisfaction for the complete supplied position.

L169  Grounds012 position.commitment canonicalArticulation [.value position] (.value position)

Require Grounds for its commitment under that very value-position task.

L171/- Scope and roles are explicitly identified relative to a claim. An actually

Explain that comparison scope and method roles concern a particular claim.

L172used method needs an explanation; unused methods are not required. The input

Only a method actually used incurs the represented role-explanation duty.

L173relation can encode contextual relevance without a universal numeric scale. -/

The relevance relation does not require a universal numerical scale.

L174inductive AssessmentMethod | measurement | repetition | framework

Introduce three represented method kinds: measurement, repetition and framework.

L175  deriving DecidableEq

Derive decidable equality for this finite method type.

L176structure ScopeAccount (W : Type) where

Package the claim-specific comparison and method-role account over W.

L177  claim : Claim W

Store the claim being assessed.

L178  conditions : Claim W

Store relevant conditions independently of observation scope.

L179  observationScope : Claim W

Store which worlds or inputs are included in observation scope.

L180  relevant : W → W → Prop

Store contextual relevance between compared objects.

L181  compared : W → W → Prop

Store which object pairs are actually compared.

L182  used : AssessmentMethod → Prop

Store which assessment methods are actually used.

L183  role : AssessmentMethod → String

Assign a stated role text to each method.

L184  explains : AssessmentMethod → String → Claim W → Claim W → Prop

Store the semantic relation connecting a method and its role text to the claim and conditions.

L186/-- organon-map CoreReader.Adopted.scopeSpecification

Begin source-tracing metadata for CoreReader.Adopted.scopeSpecification; this mapping is not a proof premise.

L187organon.grounds.scope#p1 sha256 4a0e93c7834e4ef62f129ee4621cf7bf1c93b64d86f9f145d1592adcf9fb6693

Record source clause organon.grounds.scope#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L188organon.grounds.scope#p2 sha256 4a0e93c7834e4ef62f129ee4621cf7bf1c93b64d86f9f145d1592adcf9fb6693

Record source clause organon.grounds.scope#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L189organon.grounds.scope#p3 sha256 4a0e93c7834e4ef62f129ee4621cf7bf1c93b64d86f9f145d1592adcf9fb6693

Record source clause organon.grounds.scope#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L190-/

Close the preceding source-mapping comment without adding a logical condition.

L191def scopeSpecification {W : Type} (account : ScopeAccount W) : Prop :=

Define scope satisfaction for a supplied comparison account.

L192  (∀ a b, account.compared a b → account.conditions a ∧ account.conditions b ∧

Every actual compared pair must satisfy the account's conditions on both sides.

L193    account.observationScope a ∧ account.observationScope b ∧ account.relevant a b) ∧

Both sides must also lie in scope and satisfy the stated relevance relation.

L194  ∀ method, account.used method → account.role method ≠ "" ∧

Every used method needs a nonempty role description.

L195    account.explains method (account.role method) account.claim account.conditions

That exact role must explain this method relative to this claim and its conditions.

L197/- A capability is selected by the application as an exact object-scoped

Capability is modeled by an application-selected contract for one exact process.

L198contract; whether explanation is part of it remains an application choice. -/

Requiring an explanation certificate remains an application decision.

L199/-- organon-map CoreReader.Adopted.capabilitySpecification

Begin source-tracing metadata for CoreReader.Adopted.capabilitySpecification; this mapping is not a proof premise.

L200organon.grounds.capabilities#p1 sha256 7249f6f2ef327baaa72349cae53b9245f23a34436356dd05f3c6005cab35e8f0

Record source clause organon.grounds.capabilities#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L201organon.grounds.capabilities#p2 sha256 7249f6f2ef327baaa72349cae53b9245f23a34436356dd05f3c6005cab35e8f0

Record source clause organon.grounds.capabilities#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L202organon.relationships.roles#p2 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L203organon.relationships.roles#p3 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L204-/

Close the preceding source-mapping comment without adding a logical condition.

L205def capabilitySpecification (assessed : Process) (contract : Claim Process) : Prop :=

Define a capability obligation for the assessed process and selected contract.

L206  Grounds012 contract canonicalArticulation [processContractFacet assessed contract]

Require Grounds for the exact process-contract facet.

L207    (.inferential (processScope assessed) contract)

The original inferential task fixes the process-identity assumptions and that contract.

L209/-- organon-map CoreReader.Adopted.choiceSpecification

Begin source-tracing metadata for CoreReader.Adopted.choiceSpecification; this mapping is not a proof premise.

L210organon.grounds.implementations#p1 sha256 bb2a822a304d4a20f513218f356ddbeeca8ee139e3ed802213591e9ff6c5095c

Record source clause organon.grounds.implementations#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L211organon.grounds.implementations#p2 sha256 bb2a822a304d4a20f513218f356ddbeeca8ee139e3ed802213591e9ff6c5095c

Record source clause organon.grounds.implementations#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L212organon.grounds.implementations.limits#p1 sha256 db9b5f1803baab0e1b05a3a9e068948667412afa7d692e1da3869ca54be4b870

Record source clause organon.grounds.implementations.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L213organon.relationships.roles#p3 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L214-/

Close the preceding source-mapping comment without adding a logical condition.

L215def choiceSpecification (requirements : Requirements) (implementation : Implementation)

Define choice satisfaction for actual requirements and implementation.

L216    (reasons : List Reason) : Prop := JustifiedChoice requirements implementation reasons

The reasons must satisfy the helper's feasibility and relevant-content conditions.

L218/- A collaborator supplies the successor operation. Removing that resource

The comment identifies a collaborator as the source of the additional operation.

L219leaves the initial state; progress is tested on actual added operation content. -/

Without that resource, the transition retains the initial operation content.

L220def collaborativeRevision (resources : ExternalResources) : State :=

Define the collaboration-dependent state revision.

L221  if resources.collaborator.isSome then extendedState else baseState

Return extendedState when a collaborator exists, otherwise baseState.

L223theorem collaborativeProgress :

Prove actual collaborative expansion can coexist with failure of unaided execution.

L224    generationSpecification openPolicy ∧

The open policy satisfies the represented generation commitment.

L225    Expanded baseState (collaborativeRevision availableResources) ∧

The available collaborator yields a newly constructed or understood operation.

L226    ¬ Expanded baseState (collaborativeRevision { availableResources with collaborator := none }) ∧

Removing that same collaborator removes the represented expansion.

L227    assistedExecution ⟨none, none, none⟩ = none := by

With no experience, knowledge or collaborator, assisted execution returns no result.

L228  refine ⟨⟨Or.inl rfl, fun _ _ => trivial⟩, ?_, ?_, rfl⟩

Supply the policy proof and unaided failure by evaluation, leaving both transition claims.

L229  · exact Or.inr ⟨.successor, by simp [collaborativeRevision, availableResources, extendedState],

Choose successor as the newly constructed operation in the extended state.

L230      by simp [baseState]⟩

Verify that successor was absent from the base state.

L231  · simp [collaborativeRevision, Expanded, baseState]

Expand the no-collaborator branch and show unchanged content cannot count as expansion.

L233/- A truth-preserving current slice need not retain an earlier incompatible

The comment separates current consistency from old incompatible judgments.

L234slice. Context changes and presentation order have separate semantics. -/

Semantic context changes and presentation ordering have different roles.

L235/-- organon-map CoreReader.Adopted.consistencyConsequences

Begin source-tracing metadata for CoreReader.Adopted.consistencyConsequences; this mapping is not a proof premise.

L236organon.charter.consistency#p1 sha256 c6960c590c096d33250599cf418e3c6a1dc26bfc7d7800c82b8efde656950f42

Record source clause organon.charter.consistency#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L237organon.charter.consistency.meaning#p1 sha256 81c09e38a3349499f95401d1c08f6069666c13547a43bc4e4395330743055faa

Record source clause organon.charter.consistency.meaning#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L238organon.charter.consistency.meaning#p2 sha256 81c09e38a3349499f95401d1c08f6069666c13547a43bc4e4395330743055faa

Record source clause organon.charter.consistency.meaning#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L239organon.charter.consistency.limits#p1 sha256 4fa1c29bf95ad6ef04c6d27671a832c0af8ba31b9c0d8018a8d09c4f33c38e75

Record source clause organon.charter.consistency.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L240-/

Close the preceding source-mapping comment without adding a logical condition.

L241theorem consistencyConsequences {W Q : Type} (t : Theory W) (c : Context W Q) (q : Q)

State a conditional inconsistency theorem for one theory, context and question.

L242    (positive : Consequence t c q true) (negative : Consequence t c q false) :

Assume positive and negative consequences of that same question in that same context.

L243    ¬ Consistent t c := conflictRequiresChange t c q positive negative

Those two premises directly violate Consistent; no factual correctness is inferred.

L245def broadBoolContext : Context Bool Unit := ⟨emptyTheory, onQuestion, fun _ => True⟩

Use Boolean worlds, the on-question, no extra assumptions and unrestricted scope.

L247theorem sliceConsistency :

Prove each revision slice consistent while the old/new union is inconsistent.

L248    (∀ time, Consistent (revisionSlice time) broadBoolContext) ∧

Quantify consistency over every current time slice.

L249    ¬ Consistent (union (revisionSlice 0) (revisionSlice 1)) broadBoolContext := by

Reject simultaneous retention of the opposing slices zero and one.

L250  constructor

Prove individual-slice consistency and union inconsistency separately.

L251  · intro time

Fix an arbitrary time for the positive branch.

L252    apply consequenceConsistency

Use an actual admissible world to establish consistency.

L253    exact ⟨time == 0, (modelsSingleton _ _).2 rfl, (by intro p hp; cases hp), trivial⟩

Choose the Boolean time==0; it models the slice, empty assumptions and unrestricted scope.

L254  · apply conflictRequiresChange _ _ ()

Reduce union inconsistency to opposite consequences of the on-question.

L255    · intro w h

Take an arbitrary admissible world for the positive consequence.

L256      change w = true

Expose the required positive meaning as w=true.

L257      exact (modelsSingleton (fun w : Bool => w = true) w).1 ((modelsUnion _ _ _).1 h.1).1

Read w=true from the zero-time component of the union's model.

L258    · intro w h ht

For the negative consequence, additionally assume the world is on.

L259      have hn := (modelsSingleton _ _).1 ((modelsUnion _ _ _).1 h.1).2

Read w=false from the one-time component of the same union model.

L260      cases ht.symm.trans hn

Compose the equalities to contradict true=false.

L262theorem explicitlyConsistentLimits :

Prove explicit consistent examples with false assumptions or an undecided question.

L263    Consistent (singleton (fun w : Bool => w = true)) broadBoolContext ∧

The singleton on-theory is consistent in the broad context.

L264    ¬ Models (singleton (fun w : Bool => w = true)) false ∧

Deny that actual false models the theory whose sole claim is world=true.

L265    Consistent (emptyTheory : Theory Bool) broadBoolContext ∧

The empty held theory is also consistent in that context.

L266    ¬ Entails emptyTheory (fun w : Bool => w = true) := by

The inhabited empty theory does not entail the positive true-world answer.

L267  refine ⟨?_, consistentFalse.2, ?_, consistentIncomplete.2.1⟩

Reuse the checked false-world and non-entailment results, leaving consistency witnesses.

L268  · exact consequenceConsistency _ _ ⟨true, (modelsSingleton _ _).2 rfl,

For the on-theory choose the true world as its model.

L269      (by intro p hp; cases hp), trivial⟩

Its additional assumptions are empty and its scope is unrestricted.

L270  · exact consequenceConsistency _ _ ⟨true, (by intro p hp; cases hp),

For the empty theory again choose true; no held premises must be checked.

L271      (by intro p hp; cases hp), trivial⟩

The empty contextual assumptions and unrestricted scope complete admissibility.

L273/- One observed input supports the local claim. The identical records cannot

The comment distinguishes support at input zero from stronger assertions.

L274support all inputs, nor the stronger claim that both Boolean outputs are true. -/

Neither all-input truth nor an extra input-one conjunct follows from that record.

L275def localFacet012 : Facet (Nat → Bool) :=

Define the empirical facet asserting output true only at input zero.

L276  .empirical [zeroRecord] (fun _ => True) (fun f => f 0 = true) (fun _ => True)

Use zeroRecord, unrestricted world scope, the local claim and trivial uncertainty.

L277def globalFacet012 : Facet (Nat → Bool) :=

Define the stronger all-input empirical assertion with the same record.

L278  .empirical [zeroRecord] (fun _ => True) allTrue (fun _ => True)

The claim is allTrue; neither scope nor uncertainty adds evidence.

L279def strongFacet012 : Facet (Nat → Bool) :=

Define the strengthened two-output empirical assertion.

L280  .empirical [zeroRecord] (fun _ => True) (fun f => f 0 = true ∧ f 1 = true) (fun _ => True)

Require both f0=true and f1=true from the unchanged input-zero record.

L282theorem localFacetChecked012 : FacetDischarged localFacet012 :=

Prove the local empirical facet discharged in its represented scope.

L283  ⟨⟨localGenerator 0, (zeroCompatible _).2 rfl, trivial⟩,

Give localGenerator0 as a real evidence-compatible world in scope.

L284    (fun f hf _ => (zeroCompatible f).1 hf), fun _ _ => trivial⟩

Compatibility yields its observed zero output; the uncertainty predicate is True.

L286theorem scopeStrength012 :

Bundle local support with failures of global scope and stronger claim content.

L287    Grounds012 localFacet012.claim canonicalArticulation [localFacet012] (taskOfFacet localFacet012) ∧

The local claim fulfills its explicitly declared local task.

L288    Articulated (canonicalArticulation globalFacet012) ∧

The global candidate is nevertheless clearly articulated.

L289    ¬ Grounds012 globalFacet012.claim canonicalArticulation [globalFacet012] (taskOfFacet globalFacet012) ∧

The all-input task fails Grounds despite that articulation.

L290    ¬ Grounds012 strongFacet012.claim canonicalArticulation [strongFacet012] (taskOfFacet strongFacet012) := by

The two-output task also fails with the same records.

L291  refine ⟨grounds012Singleton _ localFacetChecked012, ⟨by simp [canonicalArticulation, globalFacet012],

Reuse checked local support and begin verifying the global articulation fields.

L292    by simp [canonicalArticulation, globalFacet012]⟩, ?_, ?_⟩

Show its reasons are identifiable; leave both substantive failures to prove.

L293  · intro h

Assume global Grounds in order to refute it.

L294    have checked := (h.2 globalFacet012 (by simp)).2.2.2.1

Extract the global facet's required discharge from that hypothesis.

L295    have bad := checked.2.1 (localGenerator 0) ((zeroCompatible _).2 rfl) trivial 1

Apply its supposed support to localGenerator0 at input one, where the output is false.

L296    cases bad

Eliminate the resulting impossible Boolean equality.

L297  · intro h

Assume Grounds for the stronger two-output claim, for contradiction.

L298    have checked := (h.2 strongFacet012 (by simp)).2.2.2.1

Extract that candidate's empirical discharge obligation.

L299    have bad := (checked.2.1 (localGenerator 0) ((zeroCompatible _).2 rfl) trivial).2

Its second conjunct wrongly requires localGenerator0's input-one output to be true.

L300    cases bad

Contradict the actual false output.

L302/- A bounded outcome statement can leave another observable entirely unknown.

The comment permits one observed result while another observable remains unknown.

L303This represents uncertainty by a range of compatible worlds, not a probability. -/

Uncertainty here is a set of possible worlds, not a probability distribution.

L304def uncertainFacet012 : Facet (Bool × Bool) :=

Define an uncertain empirical facet over pairs of Booleans.

L305  .empirical [temperatureRecord, temperatureRecord] (fun _ => True)

Use repeated first-coordinate observations without restricting worlds further.

L306    (fun w => w.1 = true) (fun w => w.2 = true ∨ w.2 = false)

Assert the first coordinate true while allowing either value of the second.

L308theorem uncertainSupported012 :

Prove this limited empirical assertion and both remaining possibilities.

L309    empiricalSpecification [temperatureRecord, temperatureRecord] (fun _ => True)

The empirical task uses the same repeated temperature records.

L310      (fun w => w.1 = true) (fun w => w.2 = true ∨ w.2 = false) ∧

The claim fixes only coordinate one; uncertainty explicitly allows coordinate two to vary.

L311    Compatible [temperatureRecord, temperatureRecord] (true,true) ∧

The true/true world matches the repeated records.

L312    Compatible [temperatureRecord, temperatureRecord] (true,false) := by

The true/false world matches them as well.

L313  refine ⟨grounds012Singleton uncertainFacet012 ?_, temperatureCompatible true, temperatureCompatible false⟩

Use canonical singleton Grounds and provide both compatible worlds.

L314  refine ⟨⟨(true,false), temperatureCompatible false, trivial⟩, ?_, ?_⟩

Choose true/false as the nonempty empirical witness and separate the support duties.

L315  · intro w hw _; exact hw temperatureRecord (by simp)

Read the actual first-coordinate observation from the record membership.

L316  · intro w _; cases w.2 <;> simp

Exhaust the two second-coordinate values to prove the stated uncertainty range.

L318/- Correctly completed negative examination is distinct from a supported

The comment separates accurate negative examination from supported positive assertion.

L319conclusion. The countervaluation satisfies the same premises. -/

The countervaluation must satisfy the same original premises.

L320def InferenceExamined {W : Type} (premises : Theory W) (conclusion : Claim W)

Define an examination report for explicit premises and conclusion.

L321    (accepted : Bool) : Prop := accepted = true ↔ Entails premises conclusion

A report accepts exactly when the original premises entail the conclusion; this defines accuracy, not a positive result.

L323theorem inferenceChecked012 :

Prove a valid arithmetic inference alongside an accurate negative Boolean examination.

L324    inferentialSpecification (singleton (fun n : Nat => n = 2)) (fun n => n + 1 = 3) ∧

From the stated assumption n=2 the scoped inference establishes n+1=3.

L325    InferenceExamined (emptyTheory : Theory Bool) (fun w => w = true) false ∧

The empty Boolean theory accurately receives a negative report for the on-claim.

L326    Models (emptyTheory : Theory Bool) false ∧ ¬ ((fun w : Bool => w = true) false) := by

The false world satisfies the same empty premises while falsifying that conclusion.

L327  refine ⟨grounds012Singleton arithmeticFacet noUniversalChain.1, ?_, (by intro p hp; cases hp), by decide⟩

Use checked arithmetic discharge and the concrete counterworld, leaving report accuracy.

L328  constructor

Prove both directions of the report's equivalence with entailment.

L329  · intro h; cases h

A false report equaling true is impossible.

L330  · intro h; exact False.elim (consistentIncomplete.2.1 h)

Supposed entailment contradicts the already checked empty-theory countervaluation.

L332/- Closing a response to an actually relevant criticism fails the value

The comment identifies relevant criticism as an actual responsibility.

L333procedure even when its budget/benefit reasons and joint adoption are unchanged. -/

Unchanged budget reasons and adoption do not excuse closing the response.

L334def closedPosition012 : ValuePosition Bool := { switchPosition with response := fun _ => none }

Keep switchPosition unchanged except that every response becomes none.

L336theorem closedCriticism012 : ¬ ValueProcedure closedPosition012 := by

Prove that the response-free position fails the represented value procedure.

L337  intro h

Assume that value procedure for contradiction.

L338  obtain ⟨answer, ha, _⟩ := h.2.2.2 false trivial rfl

Apply its response duty to the actually relevant false-world criticism.

L339  cases ha

The required some answer contradicts the defined none response.

L341theorem valueFulfilled012 : valueSpecification switchPosition :=

State fulfillment of the fixed switch value-position task.

L342  grounds012Singleton _ switchValueProcedure

Use the checked switch value procedure in the canonical singleton helper.

L344/- Qualitative entailment orders claims by implication, without conversion of

The comment compares claim strength through logical implication.

L345value and empirical/inferential reasons to a common numeric scale. -/

No common numerical conversion of value and other reasons is required.

L346def ClaimNoStronger {W : Type} (weaker stronger : Claim W) : Prop := ∀ w, stronger w → weaker w

Define weaker as holding in every world in which stronger holds.

L348theorem qualitativeProportionality012 :

Prove the asymmetric implication ordering while retaining a reasoned value task.

L349    ClaimNoStronger (fun f : Nat → Bool => f 0 = true) allTrue ∧

Truth at every input implies truth at input zero.

L350    ¬ ClaimNoStronger allTrue (fun f : Nat → Bool => f 0 = true) ∧

Truth at zero does not imply truth at every input.

L351    valueSpecification switchPosition := by

The switch value task remains independently fulfilled.

L352  refine ⟨fun _ h => h 0, ?_, valueFulfilled012⟩

Specialize universal truth to zero and reuse value fulfillment; leave the converse to refute.

L353  intro h

Assume the stronger all-input claim follows from the local one.

L354  have bad := h (localGenerator 0) rfl 1

Apply that assumption to localGenerator0 and test input one.

L355  cases bad

The false input-one output contradicts the supposed implication.

L357def scopeRole012 : AssessmentMethod → String

Assign concrete explanatory text to each represented assessment method.

L358  | .measurement => "identify the output at the observed input zero"

Measurement identifies the output at the observed input zero.

L359  | .repetition => "check the same local conclusion against repeated input-zero observations"

Repetition checks the same local conclusion against repeated zero-input records.

L360  | .framework => "compare only the declared input; keep broader claims separate"

The framework separates the declared input from broader unsupported claims.

L362def scopeRoleContent012 : AssessmentMethod → Prop

Give each stated method role a proposition describing its actual contribution.

L363  | .measurement => Supports [zeroRecord] (fun f => f 0 = true)

Measurement's contribution is support for the observed zero output.

L364  | .repetition => Supports [zeroRecord, zeroRecord] (fun f => f 0 = true)

Repetition's contribution is support for that same output from duplicate records.

L365  | .framework => ¬ Supports [zeroRecord] allTrue

The framework records that those local observations do not support allTrue.

L367def localScopeAccount012 : ScopeAccount Nat where

Instantiate a complete local scope account over natural-number inputs.

L368  claim n := (localGenerator 0) n = true

The account concerns whether localGenerator0 succeeds at the input.

L369  conditions _ := True

There are no additional input conditions.

L370  observationScope n := n = 0

Only input zero belongs to the observation scope.

L371  relevant a b := a = b

The represented relevance relation requires equal inputs.

L372  compared a b := a = 0 ∧ b = 0

Actual comparison occurs only when both inputs equal zero.

L373  used _ := True

All three represented methods are used in this particular example.

L374  role := scopeRole012

Use the previously specified method-role text.

L375  explains method text claim conditions :=

Define what counts as an explanation for this account.

L376    text = scopeRole012 method ∧ claim = (fun n => localGenerator 0 n = true) ∧

Require the exact role text and the exact local-generator claim.

L377    conditions = (fun _ => True) ∧ scopeRoleContent012 method

Also require the actual conditions and the method's substantive contribution.

L379theorem scopeFulfilled012 : scopeSpecification localScopeAccount012 := by

Prove that the instantiated scope account fulfills its stated duties.

L380  constructor

Separate pair-comparison validity from used-method explanations.

L381  · intro a b h

Take any pair that the account says is compared.

L382    exact ⟨trivial, trivial, h.1, h.2, h.1.trans h.2.symm⟩

Use both zero identities to establish conditions, scope and equal-input relevance.

L383  · intro method _

Fix an arbitrary method used by this account.

L384    refine ⟨?_, rfl, rfl, rfl, ?_⟩

Supply exact role/claim/condition identities, leaving nonempty text and semantic contribution.

L385    · cases method <;> decide

Check each of the three literal role texts is nonempty.

L386    · cases method with

Split the substantive contribution by method kind.

L387      | measurement => exact singleObservation.2.2.1

Reuse the single observation's proved local support.

L388      | repetition => intro f hf; exact hf zeroRecord (by simp)

Read the zero record from repeated-record compatibility.

L389      | framework => exact singleObservation.2.2.2

Reuse the same observation's proved failure to support allTrue.

L391theorem capabilityFulfilled012 :

Prove two distinct process-contract fulfillments and an external certificate without internal explanation.

L392    capabilitySpecification outputOnlyProcess OutputContract ∧

The output-only process has Grounds for its output contract.

L393    capabilitySpecification explainedProcess FullProcessContract ∧

The explained process has Grounds for the stronger output-plus-explanation contract.

L394    (∃ certificate : ExternalCertificate outputOnlyProcess,

Exhibit an external certificate for the very output-only process.

L395      certificate.assessorId ≠ certificate.assessedId ∧ OutputContract outputOnlyProcess) ∧

Its assessor and assessed identifiers differ, and its output contract holds.

L396    ¬ ExplanationContract outputOnlyProcess := by

Nevertheless this process does not supply the explanation contract.

L397  refine ⟨grounds012Singleton _ (processContractDischarged _ _ outputCorrectByEvaluation),

Use evaluated output correctness to discharge the exact process-scoped inference.

L398    grounds012Singleton _ (processContractDischarged _ _ ?_),

Reduce the explained process's Grounds to proving its stronger contract.

L399    ⟨externalOutputCertificate, externalOutputCertificate.distinctParticipants,

Choose the actual external certificate and its proved participant distinction.

L400      externalOutputCertificate.outputCorrect⟩, outputOnlyNoExplanation⟩

Use its output proof and the established absence of an internal explanation.

L401  exact ⟨fun _ => rfl, .doubleInput, rfl, fun _ => rfl⟩

Prove all outputs by evaluation and supply the faithful doubleInput certificate.

L403/- This application asks the assessed object to predict a multiplier mechanism

The application asks this assessed object to predict the behavior of a multiplier mechanism.

L404at changed inputs and multiplier values. This is one operational understanding

The questions vary both inputs and multiplier values, giving an operational understanding task.

L405criterion selected by an application, not a definition of psychological understanding.

The criterion belongs to this application and does not define psychological understanding in general.

L406The original output and explanation alone do not answer the additional questions. -/

Original outputs and their faithful explanation do not by themselves supply answers to the extra questions.

L407structure MechanismApplication012 where

Define an application object containing its process and its responses to mechanism variations.

L408  process : Process

The process field contains the object's original output function and explanation response.

L409  answer : Nat → Nat → Nat

The answer function takes a multiplier and an input and returns the object's predicted natural-number output.

L411def mechanism012 (multiplier input : Nat) : Nat := multiplier * input

Define the mechanism's predicted result as the product of the multiplier and input.

L413def UnderstandingApplication012 (assessed : MechanismApplication012) : Prop :=

Define this application's stronger understanding contract for one assessed object.

L414  FullProcessContract assessed.process ∧

Require the same object's original process to satisfy both output correctness and faithful explanation.

L415  (∀ input, assessed.process.output input = mechanism012 2 input) ∧

Require every original output to agree with the multiplier mechanism at its original multiplier of two.

L416  ∀ multiplier input, assessed.answer multiplier input = mechanism012 multiplier input

Require correct mechanism answers for every natural-number multiplier and input, including changed values.

L418def explainedWithoutVariation012 : MechanismApplication012 :=

Define an object with a faithful explanation but a response that ignores multiplier changes.

L419  ⟨explainedProcess, fun _ input => input + input⟩

Use explainedProcess while always answering twice the input regardless of the requested multiplier.

L421def mechanismResponder012 : MechanismApplication012 :=

Define the object that answers mechanism-variation questions using the multiplication rule.

L422  ⟨explainedProcess, mechanism012⟩

Keep the same explainedProcess and supply mechanism012 as the actual answer function.

L424/- The assessment task is fixed by this very application object and the stronger

Fix the assessment task using this application object and its stronger contract.

L425contract. Identity is a scope premise; the positive case still proves the contract. -/

Object identity restricts scope; it does not assume the contract that the positive proof must establish.

L426def understandingScope012 (assessed : MechanismApplication012) : Theory MechanismApplication012 :=

Define the inferential scope for a specified application object.

L427  singleton (fun candidate => candidate = assessed)

Its sole scope premise says that the candidate equals the assessed object.

L429def understandingTask012 (assessed : MechanismApplication012) : AssessmentTask MechanismApplication012 :=

Define the original understanding assessment task for the specified object.

L430  .inferential (understandingScope012 assessed) UnderstandingApplication012

The task uses exact object-identity assumptions and the stronger understanding claim.

L432def understandingFacet012 (assessed : MechanismApplication012) : Facet MechanismApplication012 :=

Define the candidate inferential assessment facet for that same specified object.

L433  .inferential (understandingScope012 assessed) UnderstandingApplication012

The facet retains the original task's exact identity assumptions and understanding claim.

L435theorem mechanismResponderUnderstands012 : UnderstandingApplication012 mechanismResponder012 := by

Prove that the mechanism responder actually satisfies the selected understanding contract.

L436  refine ⟨⟨(fun _ => rfl), .doubleInput, rfl, (fun _ => rfl)⟩, ?_, fun _ _ => rfl⟩

Construct original output and explanation correctness and all variation answers by reduction, leaving the original multiplier agreement to prove.

L437  intro input

Take an arbitrary input for the remaining original-mechanism agreement obligation.

L438  simp [mechanismResponder012, explainedProcess, mechanism012, Nat.two_mul]

Expand the concrete definitions and use two times an input equals its sum with itself.

L440theorem explainedWithoutVariationFails012 :

State the failure theorem for the object that ignores multiplier variation.

L441    ¬ UnderstandingApplication012 explainedWithoutVariation012 := by

The conclusion denies the stronger understanding contract for that concrete object.

L442  intro h

Assume the stronger contract temporarily to derive a contradiction.

L443  have wrong := h.2.2 3 1

Specialize its required variation correctness to multiplier three and input one.

L444  change 2 = 3 at wrong

Compute the object's answer and mechanism result, turning the assumed equality into two equals three.

L445  cases wrong

Eliminate the impossible equality of these distinct natural numbers.

L447theorem understandingApplicationCases012 :

Bundle the concrete positive and negative understanding cases together with their object-scoped Grounds results.

L448    explainedWithoutVariation012.process = mechanismResponder012.process ∧

Both application objects contain exactly the same original process, so their outputs and explanation are identical.

L449    FullProcessContract explainedWithoutVariation012.process ∧

The object with wrong variation answers still satisfies the original output-and-explanation contract.

L450    ¬ UnderstandingApplication012 explainedWithoutVariation012 ∧

That object fails the stronger application understanding task.

L451    UnderstandingApplication012 mechanismResponder012 ∧

The mechanism responder satisfies that stronger task.

L452    Grounds012 UnderstandingApplication012 canonicalArticulation

Assert Grounds for the exact stronger understanding claim using canonical articulation.

L453      [understandingFacet012 mechanismResponder012] (understandingTask012 mechanismResponder012) ∧

The positive facet and the fixed original task both identify the mechanism responder.

L454    ¬ Grounds012 UnderstandingApplication012 canonicalArticulation

Deny Grounds for the same stronger understanding claim in the negative object case.

L455      [understandingFacet012 explainedWithoutVariation012] (understandingTask012 explainedWithoutVariation012) := by

The negative assessment retains that object's own fixed task and identity scope, then begins the bundled proof.

L456  refine ⟨rfl, ⟨(fun _ => rfl), .doubleInput, rfl, (fun _ => rfl)⟩,

Construct identical-process and faithful original-contract evidence directly from the shared concrete process.

L457    explainedWithoutVariationFails012, mechanismResponderUnderstands012, ?_, ?_⟩

Use the proved failure and success of the two understanding tasks, leaving their Grounds claims to prove.

L458  · apply grounds012Singleton

Apply the singleton Grounds helper to the positive facet; its declared task is exactly the fixed understanding task here.

L459    refine ⟨⟨mechanismResponder012, (modelsSingleton _ _).2 rfl⟩, ?_⟩

Use the responder itself as a model of its identity assumptions, then leave the semantic consequence to prove.

L460    intro candidate hc

Take an arbitrary candidate satisfying the fixed identity assumptions.

L461    have same := (modelsSingleton _ _).1 hc

Extract equality with the assessed responder from the singleton scope model.

L462    subst candidate

Replace the candidate with that very responder using the proved identity.

L463    exact mechanismResponderUnderstands012

Supply the already established concrete stronger contract, rather than assuming it in the scope.

L464  · intro h

Assume Grounds for the negative object temporarily to derive a contradiction.

L465    have discharged := (h.2 (understandingFacet012 explainedWithoutVariation012) (by simp)).2.2.2.1

Extract discharge of the actual negative object's singleton facet from the assumed Grounds.

L466    exact explainedWithoutVariationFails012

Apply the proved failure of the stronger understanding task for this object.

L467      (discharged.2 explainedWithoutVariation012 ((modelsSingleton _ _).2 rfl))

The supposed entailment applied to this same object's identity model would prove the failed contract, giving the contradiction.

L469/- The same exact application contract receives Grounds when its owner asserts

Self-assertion retains the same exact application contract.

L470it; external certificates change who supplies reasons, not the asserted object. -/

Changing the reason-provider does not change the object being asserted about.

L471def OwnCapability012 (owner claimant : Nat) (process : Process) (contract : Claim Process) : Prop :=

Define own-capability duty for owner, claimant, process and contract.

L472  owner = claimant ∧ capabilitySpecification process contract

Require identical owner/claimant identities and the ordinary scoped capability duty.

L474theorem ownCapability012 : OwnCapability012 7 7 outputOnlyProcess OutputContract :=

Prove owner 7 can assert its own output-only contract with these Grounds.

L475  ⟨rfl, capabilityFulfilled012.1⟩

Combine identity equality with the already checked output capability.

L477/- A complete represented Charter includes generation, whole-set consistency,

The complete represented Charter contains generation and whole-theory consistency.

L478truthful revision reporting and applicable contentful self-work on the same

It also contains truthful reporting and applicable contentful self-work.

L479system. The world type is the finite Candidate × Mode type. -/

These duties share one system over a finite Candidate×Mode world type.

L480def CompleteCharter012 (system : CoreReader.Integration.System)

Define the complete represented Charter for a supplied integration system.

L481    (world : CoreReader.Integration.World) : Prop :=

Evaluate its duties at one common finite world.

L482  generationSpecification (system.policy world) ∧

Require that system's own world-indexed policy to be generative.

L483  consistencySpecification

Also require the coupled consistency/reporting specification.

L484    ⟨CoreReader.Integration.systemHeld system, CoreReader.Integration.systemContext system, 0⟩

Use the system's whole held theory and context as the before snapshot.

L485    ⟨CoreReader.Integration.systemHeld system, CoreReader.Integration.systemContext system, 0⟩ false ∧

Use the identical after snapshot with a false change report; no change is hidden.

L486  reflexivitySpecification ((system.rules world).map legacyRule) (fun s => s.owner = system.owner)

Apply the generic reflexivity specification to this same system's mapped rules and owner.

L487    (legacyPerformed (system.rules world) (system.work world)) ∧

Use this system's actual rules and work records in the performed relation.

L488  (system.policy world).current system.method.form ∧

Require its method form to be among its current forms.

L489  (system.policy world).current system.principleForm

Require its principle form to be current as well.

L491theorem completeCharter012 : CompleteCharter012 CoreReader.Integration.actualSystem CoreReader.Integration.actual := by

Prove the concrete integration system satisfies this complete represented Charter.

L492  refine ⟨CoreReader.Integration.charterChecked.1,

Reuse the concrete system's checked generative policy.

L493    ⟨CoreReader.Integration.jointConsistent, ?_⟩,

Reuse its joint consistency, leaving truthful unchanged reporting.

L494    legacyReflexivity 0 _ _ (completeOwnWork_reflexive 0), rfl, rfl⟩

Bridge actual completed self-work and verify the two current-form identities.

L495  rintro (h | h)

Split any alleged change into semantic change or revision-identity change.

L496  · exact False.elim (h ⟨fun _ => Iff.rfl, fun _ => Iff.rfl, fun _ _ => Iff.rfl, fun _ => Iff.rfl⟩)

The identical snapshots have equal held theory, assumptions, meanings and scope, contradicting semantic change.

L497  · exact False.elim (h rfl)

The identical revision identifiers contradict the other change alternative.

L499theorem charterWithoutGrounds012 :

Prove complete Charter fulfillment does not entail this concrete unsupported Grounds task.

L500    CompleteCharter012 CoreReader.Integration.actualSystem CoreReader.Integration.actual ∧

The very concrete system/world fulfills every represented Charter component.

L501    Admissible CoreReader.Integration.held CoreReader.Integration.context CoreReader.Integration.actual ∧

It also supplies an actual admissible world for the held theory and context.

L502    Compatible [CoreReader.Integration.costAllowanceRecord] CoreReader.Integration.actual ∧

The concrete cost-allowance record is true in that world.

L503    Articulated (canonicalArticulation CoreReader.Integration.unsupportedCapabilityFacet) ∧

The proposed capability facet has identifiable canonical articulation.

L504    ¬ Supports [CoreReader.Integration.costAllowanceRecord] CoreReader.Integration.capability ∧

That true cost record cannot support the actual output capability.

L505    ¬ Grounds012 CoreReader.Integration.capability canonicalArticulation

Consequently the same capability fails Grounds with these proposed grounds.

L506      [CoreReader.Integration.unsupportedCapabilityFacet]

The candidate list contains the identified unsupported capability facet.

L507      (taskOfFacet CoreReader.Integration.unsupportedCapabilityFacet) := by

Its original task retains that facet's empirical claim and support context.

L508  refine ⟨completeCharter012, CoreReader.Integration.actualAdmissible,

Reuse the complete Charter proof and the common admissible world.

L509    (by intro r hr; cases List.mem_singleton.mp hr; rfl),

Check the singleton cost record directly against this actual world.

L510    ⟨by simp [canonicalArticulation, CoreReader.Integration.unsupportedCapabilityFacet],

Unfold the facet's canonical articulation to verify its concepts.

L511      by simp [canonicalArticulation, CoreReader.Integration.unsupportedCapabilityFacet]⟩,

Also verify its nonempty identifiable reasons.

L512    CoreReader.Integration.costDoesNotSupportOutput, ?_⟩

Reuse the substantive cost/output countermodel; leave full Grounds rejection.

L513  intro h

Assume this task satisfies Grounds, for contradiction.

L514  have checked := (h.2 CoreReader.Integration.unsupportedCapabilityFacet (by simp)).2.2.2.1

Extract the required empirical discharge for that very capability facet.

L515  exact CoreReader.Integration.costDoesNotSupportOutput (fun w hw => checked.2.1 w hw trivial)

It would imply the disproved cost-to-output support relation in the same scope.

L517/- Permission to assert is evaluated on the same claim, articulation and facets.

Permission must refer to the same claim, articulation and facets.

L518The countercase derives inadequacy from the actual unobserved output. -/

Insufficiency comes from an actual outside-observation failure.

L519def groundsPermission012 {W : Type} (enabled : Bool) (claim : Claim W)

Define a permission policy with an explicit enable flag and claim.

L520    (a : Facet W → Articulation W) (facets : List (Facet W)) (task : AssessmentTask W) : Prop :=

Retain the actual articulation, candidate facets and original task in the policy inputs.

L521  if enabled then Grounds012 claim a facets task else True

Enabled permission requires Grounds; disabling it permits every package.

L523def GroundsProvision012 (enabled : Bool) : Prop :=

Define whether the permission policy enforces represented Grounds obligations.

L524  ∀ (claim : Claim (Nat → Bool)) a facets task,

Quantify over all claims, articulations, candidate lists and original tasks in this world type.

L525    groundsPermission012 enabled claim a facets task → Grounds012 claim a facets task

Require every permitted package to satisfy Grounds for that same original task.

L527theorem groundsProvision012Meaning (enabled : Bool) : GroundsProvision012 enabled ↔ enabled = true := by

Prove this enforcing-policy property holds exactly in enabled mode.

L528  cases enabled with

Consider the two enable-flag values.

L529  | true => exact ⟨fun _ => rfl, fun _ _ _ _ _ h => h⟩

Enabled permission is Grounds itself, so the implication returns its premise.

L530  | false =>

Handle the disabled mode, which allows unsupported packages.

L531    constructor

Prove each direction of the proposed equivalence in that mode.

L532    · intro h

Assume disabled permission nevertheless enforces all Grounds duties.

L533      exact False.elim (scopeStrength012.2.2.1 (h globalFacet012.claim canonicalArticulation [globalFacet012] (taskOfFacet globalFacet012) trivial))

Apply it to the concrete unsupported global task, contradicting scopeStrength012.

L534    · intro h; cases h

The converse premise false=true is impossible.

L536/- The value rationale concerns this fixed empirical assertion task. The

The value rationale concerns one fixed empirical assertion task.

L537same task, observed grounds and concrete counterworld are retained when the

Its records and actual counterworld remain identical across modes.

L538permission policy is enabled or disabled. -/

Only the permission policy changes between enabled and disabled modes.

L539def groundsExperimentTask012 : AssessmentTask (Nat → Bool) :=

Declare the original empirical task used by the policy comparison.

L540  .empirical [zeroRecord] (fun _ => True) allTrue (fun _ => True)

It asserts allTrue from the input-zero record with unrestricted scope and trivial uncertainty.

L542noncomputable def groundsExperiment012 (enabled : Bool) : Bool :=

Define a noncomputable logical decision of actual task permission, not a runtime experiment.

L543  @decide (groundsPermission012 enabled allTrue canonicalArticulation [globalFacet012]

Ask whether this exact allTrue claim and global candidate are permitted.

L544    groundsExperimentTask012) (Classical.propDecidable _)

Keep the fixed original task and use classical propositional decidability.

L546noncomputable def groundsPosition012 : ValuePosition Bool where

Define the value position about that actual task-permission policy.

L547  Position := Bool

The alternatives are enabling or disabling the policy.

L548  Outcome := Bool

The outcome is the Boolean permission decision.

L549  adopted := true

Explicitly adopt the enabled alternative; no factual derivation of adoption is asserted.

L550  selected := id

The represented world itself identifies the selected alternative.

L551  outcome _ enabled := groundsExperiment012 enabled

Evaluate the actual fixed-task permission for that alternative.

L552  objective accepted := accepted = false

The stated objective is rejection of the unsupported assertion.

L553  constraints _ enabled := GroundsProvision012 enabled

Also require that the chosen policy enforces the represented Grounds provision.

L554  starting := singleton (fun enabled => enabled = true)

The starting assumption explicitly records adoption of enabled mode.

L555  reasons := [fun _ _ => Compatible [zeroRecord] (localGenerator 0) ∧ ¬ allTrue (localGenerator 0)]

The reason is a concrete record-compatible program that falsifies allTrue, not enabled=true.

L556  limits _ := True

The represented value position has unrestricted world scope.

L557  relevantCriticism _ := ¬ Supports [zeroRecord] allTrue

The actual lack of allTrue support is a relevant criticism.

L558  response _ := some "retain local support and reject the unsupported universal conclusion"

Provide a nonempty response retaining local support and rejecting overreach.

L560theorem groundsPosition012Checked : ValueProcedure groundsPosition012 := by

Prove the finite value procedure for this concrete permission rationale.

L561  refine ⟨by simp [groundsPosition012], ?_, ?_, ?_⟩

Verify nonempty reasons and separate joint adoption, consequences and criticism response.

L562  · refine ⟨true, (modelsSingleton _ _).2 rfl, trivial, rfl, ?_⟩

Choose the enabled world, satisfying its starts, scope and adopted selection.

L563    intro reason hr

Take an arbitrary member of the position's reason list.

L564    cases List.mem_singleton.mp hr

Identify it with the singleton concrete counterworld reason.

L565    refine ⟨(zeroCompatible _).2 rfl, ?_⟩

Supply record compatibility and leave falsity of the global claim.

L566    intro h; have bad := h 1; cases bad

At input one the program outputs false, refuting allTrue.

L567  · intro w _ _ reasons

For the consequence branch assume the supplied reason facts at the current world.

L568    have counterworld := reasons _ (List.mem_singleton.mpr rfl)

Extract the actual counterworld fact from those passed reasons.

L569    change Compatible [zeroRecord] (localGenerator 0) ∧ ¬ allTrue (localGenerator 0) at counterworld

Expose its two contents: record compatibility and failure of allTrue.

L570    have unsupported : ¬ Grounds012 allTrue canonicalArticulation [globalFacet012] groundsExperimentTask012 := by

Derive lack of Grounds for the same fixed original global task.

L571      intro h

Assume that exact Grounds package for contradiction.

L572      have discharged := (h.2 globalFacet012 (by simp)).2.2.2.1

Extract its empirical discharge for globalFacet012.

L573      exact counterworld.2 (discharged.2.1 (localGenerator 0) counterworld.1 trivial)

Use the passed counterworld's compatibility to contradict its passed global falsity.

L574    refine ⟨?_, (groundsProvision012Meaning true).2 rfl⟩

Separate actual rejection from enabled enforcement of the general provision.

L575    exact @decide_eq_false (groundsPermission012 true allTrue canonicalArticulation [globalFacet012]

Turn the derived lack of permission into a false logical decision.

L576      groundsExperimentTask012) (Classical.propDecidable _) unsupported

The decision still concerns the same original task; classical decidability adds no empirical test.

L577  · intro w _ _; exact ⟨_, rfl, by decide⟩

Supply the fixed nonempty response for any relevant criticism in scope.

L579theorem groundsRationaleExperiment012 :

Prove the finite permission-policy comparison retains actual counterexample content.

L580    Compatible [zeroRecord] (localGenerator 0) ∧ ¬ allTrue (localGenerator 0) ∧

The same program matches the observed record and fails the global claim.

L581    groundsExperiment012 true = false ∧ groundsExperiment012 false = true ∧

Enabled permission rejects that task; disabled permission accepts it.

L582    groundsPosition012.outcome true true = groundsExperiment012 true ∧

The value position's enabled outcome is the actual enabled permission decision.

L583    groundsPosition012.outcome true false = groundsExperiment012 false := by

Its disabled outcome likewise is the actual disabled permission decision.

L584  refine ⟨(zeroCompatible _).2 rfl, ?_, ?_, ?_, rfl, rfl⟩

Provide compatibility and outcome identities, leaving falsity and both decisions.

L585  · intro h; have bad := h 1; cases bad

Refute allTrue by the actual failure at input one.

L586  · have actualReasons : ∀ reason ∈ groundsPosition012.reasons, reason true groundsPosition012.adopted := by

Construct every required reason explicitly at the enabled world.

L587      intro reason member

Take a reason together with its membership proof.

L588      cases List.mem_singleton.mp member

Identify it with the actual singleton counterworld reason.

L589      refine ⟨(zeroCompatible _).2 rfl, ?_⟩

Supply its observed-record compatibility.

L590      intro h; have bad := h 1; cases bad

Supply its actual allTrue counterexample at input one.

L591    exact (groundsPosition012Checked.2.2.1 true ((modelsSingleton _ _).2 rfl) trivial actualReasons).1

Apply the checked value procedure with those actual reasons and extract its rejection consequence.

L592  · exact @decide_eq_true (groundsPermission012 false allTrue canonicalArticulation [globalFacet012]

For disabled mode, the permission proposition is True.

L593      groundsExperimentTask012) (Classical.propDecidable _) trivial

Convert that trivial permission for the unchanged task into a true decision.

L595theorem groundsOnGrounds012 :

Prove a scoped value-based Grounds assessment of the represented Grounds provision itself.

L596    Grounds012 (fun enabled => GroundsProvision012 enabled) canonicalArticulation [.value groundsPosition012] (.value groundsPosition012) ∧

The assessed claim is enforcement of Grounds, with the exact groundsPosition012 value task.

L597    groundsPosition012.limits true ∧ groundsPosition012.relevantCriticism true := by

The adopted world lies in scope and has a live support-limit criticism.

L598  have same : (Facet.value groundsPosition012).claim = (fun enabled => GroundsProvision012 enabled) := by

Relate the position's adopted-selection claim to the enforcement proposition.

L599    funext enabled

Compare these claim functions at an arbitrary enabled flag.

L600    exact propext (groundsProvision012Meaning enabled).symm

Use the proved equivalence of enforcement and enabled selection, via propositional extensionality.

L601  refine ⟨?_, trivial, singleObservation.2.2.2⟩

Supply scope and actual criticism, leaving Grounds for the provision.

L602  rw [← same]

Rewrite the claim using the established exact function identity.

L603  exact grounds012Singleton _ groundsPosition012Checked

Apply singleton Grounds to the actually checked value procedure.

L605theorem reflexiveTargets012 :

Prove concrete applicable self-target coverage without universalizing applicability.

L606    reflexivitySpecification ((ownRules 0).map legacyRule) (fun s => s.owner = 0)

The full registered own rules satisfy the generic reflexivity interface.

L607      (legacyPerformed (ownRules 0) (completeOwnWork 0)) ∧

Their actual completed work supplies the performed applications.

L608    (∀ phase, Performed (completeOwnWork 0) (.process 0 0 phase) .assessment) ∧

Assessment records exist for formation, application and revision phases.

L609    Performed (completeOwnWork 0) (.system 0) .assessment ∧

There is also an actual system-self assessment.

L610    reflexivitySpecification ([applicationRule].map legacyRule) (fun s => s.owner = 0)

A narrower application-only rule separately satisfies generic reflexivity.

L611      (legacyPerformed [applicationRule] applicationWork) ∧

Its actual applicationWork is the source of performed work.

L612    ¬ Performed applicationWork (.system 0) .assessment := by

That narrower rule need not produce an inapplicable system assessment.

L613  refine ⟨legacyReflexivity 0 _ _ (completeOwnWork_reflexive 0), ?_,

Bridge complete own-work reflexivity, leaving the phase quantifier.

L614    ownAssessmentPerformed 0 (.system 0) (by simp [ownSubjects]),

Use the concrete system target's membership to obtain its assessment record.

L615    legacyReflexivity 0 _ _ applicationWork_reflexive, (applicabilityRetained 0 [] []).2.2.2⟩

Bridge the application-only example and retain the proved absent system work.

L616  intro phase

Fix an arbitrary formation/application/revision phase.

L617  apply ownAssessmentPerformed

Reduce its required record to the existing ownAssessmentPerformed theorem.

L618  cases phase <;> simp [ownSubjects]

Check the target list contains the process in each of the three phases.

L620theorem achievementSupported012 :

Prove achievement support for the exact actual transition and reject support from mere reporting.

L621    Grounds012 transitionAchievement canonicalArticulation [transitionFacet] (taskOfFacet transitionFacet) ∧

The transition's performance facet fulfills the exact achievement task it declares.

L622    Compatible [transitionPerformanceRecord] .extend ∧

The extending transition matches the actual performance record.

L623    transitionAchievement .extend ∧ ¬ transitionAchievement .inflate ∧

Extension adds capability; inventory inflation does not.

L624    ¬ Supports [transitionReportRecord] transitionAchievement := by

A report alone fails to support the same transition-achievement claim.

L625  refine ⟨grounds012Singleton _ transitionFacetDischarged, ?_, ?_, ?_, transitionReportDoesNotSupport.2.2⟩

Reuse the checked transition facet and report counterexample, leaving actual transition facts.

L626  · exact (transitionPerformanceCompatible .extend).mpr rfl

Use the equivalence between performance compatibility and the extend transition.

L627  · simp [transitionAchievement, transitionBefore, transitionAfter, Expanded, baseState, extendedState]

Expand the actual before/after states and verify the new operation in extension.

L628  · simp [transitionAchievement, transitionBefore, transitionAfter, Expanded, baseState, inflatedState]

Expand inflation and verify that neither understood nor constructed operations grow.

L630theorem semanticOrder012 : ∀ p q : Claim Bool,

State order independence for any two Boolean-world claims.

L631    ∀ r, union (singleton p) (singleton q) r ↔ union (singleton q) (singleton p) r :=

Each member belongs to one singleton union exactly when it belongs to the reversed union.

L632  representationOrderIrrelevant

Apply the general representation-order theorem.

L634def clearFalseArgument012 : Articulation Bool :=

Define a clearly stated but possibly false argument about the switch.

L635  ⟨["the actual switch is on"], singleton (fun w => w = true), [fun w => w = true], fun _ => True⟩

Its concepts, sole on-assumption, on-reason and unrestricted limit are all explicit.

L637theorem clearFalseReason012 :

Prove clear articulation does not make that argument true in the actual off-world.

L638    Articulated clearFalseArgument012 ∧ ¬ Models clearFalseArgument012.assumptions false :=

Its fields are identifiable, but the false world does not model its assumptions.

L639  ⟨⟨by simp [clearFalseArgument012], by simp [clearFalseArgument012]⟩, consistentFalse.2⟩

Check nonempty articulation and reuse the concrete false-assumption result.

L641def valueNeutralRecord012 : Record Bool := ⟨fun _ => true, true⟩

Define a record whose test always returns true and says nothing about selection.

L643theorem valueNotFact012 :

Prove a reasoned value commitment need not follow from neutral recorded facts.

L644    valueSpecification switchPosition ∧

The switch value task has its own fulfilled reasons and responsibilities.

L645    Compatible [valueNeutralRecord012] false ∧

The opposite selection false is compatible with the neutral record.

L646    ¬ Supports [valueNeutralRecord012] switchPosition.commitment ∧

Thus those records do not establish adoption of the switch commitment.

L647    ¬ Entails (emptyTheory : Theory Bool) switchPosition.commitment := by

Nor is that adoption entailed by an empty factual theory.

L648  have compatible : Compatible [valueNeutralRecord012] false := by

Construct the neutral record's actual false-selection counterworld.

L649    intro r hr; cases List.mem_singleton.mp hr; rfl

The singleton constant-true test matches its recorded result by evaluation.

L650  refine ⟨valueFulfilled012, compatible, ?_, valueWithoutSelfProof.2.2.1⟩

Reuse value fulfillment and no-selfproof, leaving the observation-support failure.

L651  intro h

Assume that neutral record supports the adoption claim.

L652  have bad := h false compatible

Apply it to the compatible opposite-selection world.

L653  cases bad

The claimed true selection conflicts with the actual false selection.

L655def wrongExplanation012 : Implementation := { identityImpl with explanation := fun n => n + 1 }

Keep identity implementation behavior and costs, but replace its explanation by successor.

L657theorem internalReasonDistinguishes012 :

Prove internal explanation fidelity distinguishes otherwise feasible equal-output implementations.

L658    (∀ n, identityImpl.run n = wrongExplanation012.run n) ∧

Both implementations return identical actual outputs at every input.

L659    Feasible identityRequirements identityImpl ∧ Feasible identityRequirements wrongExplanation012 ∧

Both meet the same output and budget feasibility requirements.

L660    Relevant identityRequirements identityImpl (.method .explanation) ∧

The identity implementation's explanation is a relevant faithful reason.

L661    ¬ Relevant identityRequirements wrongExplanation012 (.method .explanation) := by

The altered explanation fails that same relevance/content test.

L662  refine ⟨fun _ => rfl, identityFeasible, identityFeasible, internalReasons.1, ?_⟩

Supply equal outputs, both feasibility proofs and the valid explanation reason.

L663  intro h

Assume the altered explanation were a relevant faithful reason.

L664  have bad := h.2 0 trivial

Specialize its required explanation/output equality to input zero.

L665  cases bad

Successor's one output contradicts identity's zero output.

L667theorem inventoryCases012 : ∀ kind : InventoryKind,

Quantify the duplication example over every inventory category.

L668    Available [⟨kind, .copy⟩, ⟨kind, .copy⟩] .copy ∧

Two copies of a copy item still provide the copy operation.

L669    ¬ Available [⟨kind, .copy⟩, ⟨kind, .copy⟩] .successor := by

They do not provide the distinct successor operation.

L670  intro kind

Fix any document, term, tool or artifact category.

L671  simp [Available]

Unfold actual item membership to check the operation content.

L674def selfExemptRule012 : ReflexiveRule Nat Nat Bool :=

Define an assessment rule applicable to every natural-number target.

L675  ⟨⟨0,1⟩, .assessment, fun _ => True, id,

Give it key (0,1), universal applicability and the target itself as input.

L676    fun input output => output = ownArithmeticPrinciple input⟩

Its outcome must equal actual evaluation of ownArithmeticPrinciple at that input.

L677def selfExemptPerformed012 (key : PrincipleKey) (target input : Nat) (output : Bool) : Prop :=

Define the actual work relation for this deliberately self-exempt rule.

L678  key = ⟨0,1⟩ ∧ target = 1 ∧ input = target ∧ output = ownArithmeticPrinciple input

Work exists only for target one, with matching key/input and an evaluated arithmetic result.

L680theorem openSelfExempt012 :

Prove open revisability plus real work on another target does not satisfy self-application.

L681    generationSpecification openPolicy ∧ openPolicy.revisable ⟨.principle,0⟩ ∧

The policy values expansion and keeps the principle form revisable.

L682    selfExemptPerformed012 ⟨0,1⟩ 1 1 true ∧

An actual assessment of target one returns true.

L683    selfExemptRule012.applicable 0 ∧

Nevertheless the same rule is applicable to self-target zero.

L684    ¬ reflexivitySpecification [selfExemptRule012] (fun target => target = 0) selfExemptPerformed012 := by

It fails reflexivity because that applicable self-target receives no work.

L685  refine ⟨⟨Or.inl rfl, fun _ _ => trivial⟩, trivial, ⟨rfl,rfl,rfl,by decide⟩, trivial, ?_⟩

Supply actual policy/revisability and other-target work, leaving self-duty failure.

L686  intro h

Assume reflexivity for this self-exempt relation.

L687  obtain ⟨outcome, performed, _⟩ := h.2 selfExemptRule012 (by simp) 0 rfl trivial

Obtain its supposedly performed outcome at applicable self-target zero.

L688  cases performed.2.1

Performed requires target zero to equal one, a contradiction.

L690theorem ownPhilosophyStatus012 :

Prove the system's current philosophy method receives no status-only privilege.

L691    ¬ choiceSpecification CoreReader.Integration.proposalRequirements

Begin the status-only rejection under the actual proposal-review requirements.

L692      (CoreReader.Integration.currentPhilosophy CoreReader.Integration.actualSystem CoreReader.Integration.actual).implementation

Use exactly the same current philosophy implementation in this status-only negative branch.

L693      [.status .standing] ∧

The rejected reason list contains standing alone.

L694    choiceSpecification CoreReader.Integration.proposalRequirements

State the contrasting justified choice under the same proposal-review requirements.

L695      (CoreReader.Integration.currentPhilosophy CoreReader.Integration.actualSystem CoreReader.Integration.actual).implementation

Use exactly the same current philosophy implementation in the positive case.

L696      [.method .output] :=

Its actual output performance supplies the positive reason.

L697  ⟨CoreReader.Integration.existingPhilosophyNotPrivileged.2.2.1,

Reuse the checked status-only rejection for the actual current method.

L698    CoreReader.Integration.existingPhilosophyNotPrivileged.2.2.2.1⟩

Reuse its separate checked output-based justification.

L700def jointContext012 : Context (Bool × Bool) Unit :=

Define one joint context over two Boolean coordinates.

L701  ⟨emptyTheory, fun _ w => w.2 = true, fun _ => True⟩

Use no extra assumptions; the question asks whether coordinate two is true, at unrestricted scope.

L703theorem jointImplicationConflict012 :

Derive both question signs from the jointly held premises and prove inconsistency.

L704    Consequence jointTheory jointContext012 () true ∧

The joint theory implies the positive second-coordinate question.

L705    Consequence jointTheory jointContext012 () false ∧

It also implies that same question's negation in the same context.

L706    ¬ Consistent jointTheory jointContext012 := by

Therefore it violates the defined consistency condition.

L707  have positive : Consequence jointTheory jointContext012 () true := by

First derive the positive consequence from the actual combined premises.

L708    intro w hw

Take an arbitrary admissible world for the whole joint theory.

L709    exact (hw.1 premiseRule (Or.inr (Or.inl rfl))) (hw.1 premiseP (Or.inl rfl))

Extract P→Q and P from the same held set and apply the former to the latter.

L710  have negative : Consequence jointTheory jointContext012 () false := by

Then derive the negative consequence from the same theory.

L711    intro w hw

Use the same whole-theory admissibility condition.

L712    exact hw.1 premiseNotQ (Or.inr (Or.inr rfl))

Read the held ¬Q premise through its exact nested-union membership.

L713  exact ⟨positive, negative, conflictRequiresChange _ _ () positive negative⟩

Combine both signs and apply the general contradiction criterion; no explosion rule is used.

L715def tensionContext012 : Context Nat Unit :=

Define a numerical budget context for simultaneous-value tension.

L716  ⟨emptyTheory, fun _ n => n ≤ 6, fun _ => True⟩

The question is n≤6 with no extra assumptions and unrestricted scope.

L718theorem tensionConsistent012 :

Prove the two different budget demands are jointly consistent.

L719    Consistent (union (singleton (fun n : Nat => 4 ≤ n)) (singleton (fun n => n ≤ 6))) tensionContext012 := by

The whole held set requires 4≤n and n≤6 simultaneously.

L720  apply consequenceConsistency

Establish consistency by an explicit admissible allocation.

L721  exact ⟨5, (modelsUnion _ _ _).2 ⟨(modelsSingleton _ _).2 (by decide),

Choose five, satisfying the first budget demand in the union.

L722    (modelsSingleton _ _).2 (by decide)⟩, (by intro p hp; cases hp), trivial⟩

Also satisfy the second demand, empty assumptions and unrestricted scope.

L724theorem qualitativeUnmeasured012 :

Prove a qualitative inference without an observation method.

L725    inferentialSpecification (singleton (fun on : Bool => on = true)) (fun on => on ≠ false) ∧

Under the explicit premise on=true, infer on≠false.

L726    usesObservation (Facet.inferential (singleton (fun on : Bool => on = true)) (fun on => on ≠ false)) = false := by

The actual inferential facet reports that it does not use observation.

L727  refine ⟨grounds012Singleton _ ⟨⟨true, (modelsSingleton _ _).2 rfl⟩, ?_⟩, rfl⟩

Provide the true-world premise model and leave the required inference.

L728  intro on hon hf

Take a premise-satisfying Boolean and suppose it equals false.

L729  have ht := (modelsSingleton (fun on : Bool => on = true) on).1 hon

Read its equality to true from the singleton premise theory.

L730  cases ht.symm.trans hf

The two equalities would identify true with false.

L733theorem allStatusOnly012 : ∀ kind : StatusKind,

Quantify status-only rejection over every represented status kind.

L734    ¬ choiceSpecification identityRequirements identityImpl [.status kind] :=

Neither name, convention nor standing alone justifies the identity implementation.

L735  statusOnlyFails identityRequirements identityImpl

Apply the helper's all-kind status-only theorem to these exact requirements and implementation.

L737/- A finite two-draw experiment assigns positive equal weights to both possible

The comment states that both finite possible draws receive positive equal weights.

L738outcomes. It models possibility and a stable conclusion, not empirical claims

The model concerns possible varying outcomes and a stable bound.

L739about any physical random-number source. -/

It makes no empirical assertion about a physical randomness source.

L740def drawWeight012 (_draw : Bool) : Nat := 1

Assign weight one to each Boolean draw.

L741def randomTrial012 (draw : Bool) : Trial :=

Define the actual and recorded outcome for each draw.

L742  ⟨0, if draw then 1 else 2, if draw then 1 else 2⟩

Both draws use setting zero; true gives outcome one and false gives two, recorded accurately.

L744theorem randomOutcomes012 :

Prove the finite draws vary without losing setting reproducibility or their bound.

L745    drawWeight012 true > 0 ∧ drawWeight012 false > 0 ∧

Both possible draw weights are positive.

L746    drawWeight012 true = drawWeight012 false ∧

The two weights are equal.

L747    Reproduced (randomTrial012 true) (randomTrial012 false) ∧

Both trials reproduce the same setting.

L748    (randomTrial012 true).actualOutcome ≠ (randomTrial012 false).actualOutcome ∧

Their actual outcomes nevertheless differ.

L749    (∀ draw, Verified (randomTrial012 draw) ∧ Bounded (randomTrial012 draw)) := by

For every draw the record is accurate and the actual outcome is at most two.

L750  refine ⟨by decide, by decide, rfl, rfl, by decide, ?_⟩

Evaluate positive weights, equality, settings and different outcomes; leave the universal verification/bound.

L751  intro draw

Fix an arbitrary draw.

L752  cases draw <;> simp [Verified, Bounded, randomTrial012]

Check both draws by unfolding actual records and bounds.

L755/- Original tasks are fixed independently of the candidate substitutions below. -/

Original assessment tasks are declared before and independently of the proposed substitutions.

L756def originalGlobalTask012 : AssessmentTask (Nat → Bool) :=

Define the fixed original all-input empirical task.

L757  .empirical [zeroRecord] (fun _ => True) allTrue (fun _ => True)

Its only observation is zeroRecord; its claim is allTrue.

L758def originalLocalTask012 : AssessmentTask (Nat → Bool) :=

Define the different original local empirical task.

L759  .empirical [zeroRecord] (fun _ => True) (fun f => f 0 = true) (fun _ => True)

With the same record it asserts only f0=true.

L761def circularGlobalFacet012 : Facet (Nat → Bool) := .inferential (singleton allTrue) allTrue

Define a circular but mathematically valid conditional inference: assume allTrue and conclude allTrue.

L763theorem circularGlobalConditional012 : FacetDischarged circularGlobalFacet012 := by

Prove that separately stated conditional inference is satisfiable and valid.

L764  refine ⟨⟨fun _ => true, (modelsSingleton _ _).2 (fun _ => rfl)⟩, ?_⟩

The constant-true function satisfies its allTrue assumption.

L765  intro f hf

Take an arbitrary function modeling that singleton assumption.

L766  exact (modelsSingleton _ _).1 hf

Return the allTrue fact already present in the premise model.

L768theorem circularSubstitutionRejected012 :

Distinguish valid fulfillment of the new conditional task from an invalid substitution into the original empirical task.

L769    Grounds012 allTrue canonicalArticulation [circularGlobalFacet012] (taskOfFacet circularGlobalFacet012) ∧

The circular facet has Grounds for its own explicitly new conditional task.

L770    ¬ NatureAppropriate originalGlobalTask012 circularGlobalFacet012 ∧

It is not appropriate to the previously fixed global empirical task.

L771    ¬ Grounds012 allTrue canonicalArticulation [circularGlobalFacet012] originalGlobalTask012 := by

Thus it cannot fulfill that original task merely by sharing its conclusion.

L772  have inappropriate : ¬ NatureAppropriate originalGlobalTask012 circularGlobalFacet012 := by

First prove the candidate violates original-task appropriateness.

L773    intro h

Assume appropriateness for contradiction.

L774    have equalPremises := h.1

Extract its demanded equality of original and candidate premise theories.

L775    have originalMember : singleton (fun f => Compatible [zeroRecord] f ∧ True) allTrue := equalPremises ▸ (show singleton allTrue allTrue from rfl)

That equality would make allTrue a member of the observation-and-scope singleton theory.

L776    have equalClaims : allTrue = (fun f => Compatible [zeroRecord] f ∧ True) := originalMember

Singleton membership then equates allTrue itself with mere record compatibility and scope.

L777    have claimedAll := (congrFun equalClaims (localGenerator 0)).mpr ⟨(zeroCompatible _).2 rfl, trivial⟩

Apply that false identification to localGenerator0, which really matches the original record.

L778    have bad := claimedAll 1

The identification incorrectly yields true output at input one.

L779    cases bad

Contradict the actual false output.

L780  refine ⟨grounds012Singleton _ circularGlobalConditional012, inappropriate, ?_⟩

Retain the valid separate conditional task and the proved inappropriateness.

L781  intro h

Assume the candidate nonetheless fulfills original-task Grounds.

L782  exact inappropriate (h.2 circularGlobalFacet012 (by simp)).2.2.2.2

Extract its required appropriateness, contradicting the preceding counterexample.

L784def observedPremises012 : Theory (Nat → Bool) := singleton (fun f => Compatible [zeroRecord] f ∧ True)

Fix inference premises to exactly original zero-record compatibility and scope.

L785def observedInferenceFacet012 : Facet (Nat → Bool) :=

Define a candidate inference using those unchanged original premises.

L786  .inferential observedPremises012 (fun f => f 0 = true)

Conclude only the actual zero-input observation.

L788theorem observedInferenceChecked012 : FacetDischarged observedInferenceFacet012 := by

Prove this observation-based inference satisfiable and valid.

L789  refine ⟨⟨localGenerator 0, (modelsSingleton _ _).2 ⟨(zeroCompatible _).2 rfl, trivial⟩⟩, ?_⟩

Use localGenerator0 as a model of the original record/scope premises.

L790  intro f hf

Take any function satisfying those exact premises.

L791  exact (zeroCompatible _).1 ((modelsSingleton _ _).1 hf).1

Extract compatibility and hence the observed zero output.

L793theorem sameEmpiricalTaskTwoMethods012 :

Prove two assessment forms can fulfill one unchanged empirical task.

L794    Grounds012 (fun f => f 0 = true) canonicalArticulation [localFacet012] originalLocalTask012 ∧

The original empirical facet fulfills the fixed local task.

L795    Grounds012 (fun f => f 0 = true) canonicalArticulation [observedInferenceFacet012] originalLocalTask012 := by

The legitimate observation-based inference fulfills that very same task.

L796  refine ⟨grounds012Singleton _ localFacetChecked012, ?_⟩

Reuse the original empirical proof and leave the alternative inference adapter.

L797  refine ⟨by simp, ?_⟩

Show the alternative candidate list nonempty and check its sole member.

L798  intro f hf

Take any candidate in that list.

L799  cases List.mem_singleton.mp hf

Identify it with the observation-based inference facet.

L800  exact ⟨rfl, canonicalArticulated _ observedInferenceChecked012,

Supply exact conclusion and canonical articulation for the checked inference.

L801    canonicalFacetArticulated _, observedInferenceChecked012, rfl, rfl, fun _ _ => trivial⟩

Retain original premises, conclusion and the original trivial uncertainty support.

L803/- The second coordinate remains unobserved. Switching assessment form cannot

The second coordinate is not observed by these records.

L804remove that uncertainty responsibility from the original empirical task. -/

Changing to inference cannot erase that original uncertainty obligation.

L805def originalUncertaintyTask012 : AssessmentTask (Bool × Bool) :=

Define an original task demanding more uncertainty support than the records provide.

L806  .empirical [temperatureRecord, temperatureRecord] (fun _ => True)

Use repeated first-coordinate records with unrestricted scope.

L807    (fun w => w.1 = true) (fun w => w.2 = true)

Assert the first coordinate true but also demand that uncertainty establish the unobserved second as true.

L808def uncertaintyBypassFacet012 : Facet (Bool × Bool) :=

Define an inference candidate that omits this extra uncertainty duty from its own discharge.

L809  .inferential (singleton (fun w => Compatible [temperatureRecord, temperatureRecord] w ∧ True))

Its premises preserve the original record compatibility and scope.

L810    (fun w => w.1 = true)

Its conclusion asserts only coordinate one.

L812theorem uncertaintyBypassChecked012 : FacetDischarged uncertaintyBypassFacet012 := by

Prove that this candidate's conditional inference is itself valid.

L813  refine ⟨⟨(true,false), (modelsSingleton _ _).2 ⟨temperatureCompatible false, trivial⟩⟩, ?_⟩

The true/false world models the exact inference premises.

L814  intro w hw

Take an arbitrary model of those premises.

L815  exact ((modelsSingleton _ _).1 hw).1 temperatureRecord (by simp)

Read the recorded first-coordinate result, establishing the local conclusion.

L817theorem uncertaintySubstitutionRejected012 :

Prove that this valid inference cannot bypass the original uncertainty responsibility.

L818    FacetDischarged uncertaintyBypassFacet012 ∧

Retain the valid candidate's own discharge.

L819    ¬ NatureAppropriate originalUncertaintyTask012 uncertaintyBypassFacet012 ∧

Reject its appropriateness to the full original uncertainty task.

L820    ¬ Grounds012 (fun w : Bool × Bool => w.1 = true) canonicalArticulation

Reject Grounds for this original first-coordinate assertion and its unchanged articulation.

L821      [uncertaintyBypassFacet012] originalUncertaintyTask012 := by

The candidate must still be checked against the full original uncertainty task.

L822  have inappropriate : ¬ NatureAppropriate originalUncertaintyTask012 uncertaintyBypassFacet012 := by

First establish substantive inappropriateness.

L823    intro h

Assume the original uncertainty duty was retained and fulfilled.

L824    have bad := h.2.2 (true,false) (temperatureCompatible false)

Apply its required second-coordinate support to the record-compatible true/false world.

L825    cases bad

The false second coordinate contradicts that supposed support.

L826  exact ⟨uncertaintyBypassChecked012, inappropriate,

Combine valid conditional inference with its original-task inappropriateness.

L827    fun h => inappropriate (h.2 uncertaintyBypassFacet012 (by simp)).2.2.2.2⟩

Any claimed Grounds would supply precisely the disproved appropriateness.

L829def selectedFactFacet012 : Facet Bool :=

Define an empirical observation of which value option was actually selected.

L830  .empirical [switchRecord] (fun _ => True) switchPosition.commitment (fun _ => True)

The switch record supports the selection fact, with trivial uncertainty.

L832theorem valueFactSubstitutionRejected012 :

Separate supported selection facts from fulfillment of the original value-reason task.

L833    FacetDischarged selectedFactFacet012 ∧ valueSpecification switchPosition ∧

The empirical selection facet is discharged and the reasoned value position independently fulfills its task.

L834    ¬ Grounds012 switchPosition.commitment canonicalArticulation [selectedFactFacet012] (.value switchPosition) := by

The empirical fact alone nevertheless cannot fulfill the fixed value-position task.

L835  refine ⟨switchEmpiricalDischarged, valueFulfilled012, ?_⟩

Reuse empirical and value proofs, leaving rejection of substitution.

L836  intro h

Assume empirical facts fulfilled that original value task.

L837  exact (h.2 selectedFactFacet012 (by simp)).2.2.2.2

The required value-task/empirical-facet pairing is False in the finite adapter.

L839theorem inferentialContextSubstitutionRejected012 :

Prove that changing original inference assumptions also invalidates task substitution.

L840    FacetDischarged (Facet.inferential (singleton (fun w : Bool => w = true)) (fun w => w = true)) ∧

The conditional inference from on=true to itself is valid in its own right.

L841    ¬ Grounds012 (fun w : Bool => w = true) canonicalArticulation

Reject Grounds for the original on-claim when the inference context has been substituted.

L842      [.inferential (singleton (fun w => w = true)) (fun w => w = true)]

The proposed candidate assumes the conclusion itself as its premise.

L843      (.inferential emptyTheory (fun w => w = true)) := by

The fixed original task instead contains an empty assumption theory.

L844  refine ⟨⟨⟨true, (modelsSingleton _ _).2 rfl⟩, fun w hw => (modelsSingleton (fun w : Bool => w = true) w).1 hw⟩, ?_⟩

Give the valid conditional its true-world model and return its own premise; leave substitution failure.

L845  intro h

Assume original-task Grounds for the altered-premise candidate.

L846  have appropriate := (h.2 (.inferential (singleton (fun w : Bool => w = true)) (fun w => w = true)) (by simp)).2.2.2.2

Extract appropriateness for the exact candidate in its singleton list.

L847  have same : singleton (fun w : Bool => w = true) = emptyTheory := appropriate.1

It would equate the nonempty on-assumption singleton with the empty theory.

L848  have bad : emptyTheory (fun w : Bool => w = true) := same ▸ (show singleton (fun w : Bool => w = true) (fun w => w = true) from rfl)

Transport singleton membership to obtain membership in the empty theory.

L849  exact bad

Such membership is False by definition, completing the contradiction.

L852/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L853/-- organon-map CoreReader.Adopted.generationCases

Begin source-tracing metadata for CoreReader.Adopted.generationCases; this mapping is not a proof premise.

L854organon.charter.overview#p2 sha256 75d7d941d3c07ea748c4a9261d36a75fbd5664ff9c817c4034a9a36a3a12664c

Record source clause organon.charter.overview#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L855organon.charter.overview#p3 sha256 75d7d941d3c07ea748c4a9261d36a75fbd5664ff9c817c4034a9a36a3a12664c

Record source clause organon.charter.overview#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L856organon.charter.self-transcendence#p1 sha256 f4ca590e2ae15e3882f70c7b2bc46a8911c97cee547c8b137b5493fbf862c8c0

Record source clause organon.charter.self-transcendence#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L857organon.charter.self-transcendence.orientation#p1 sha256 7f9b85c0816b3d69e417cf3cbe17b7b59931388f84d799ce6730c998037358bf

Record source clause organon.charter.self-transcendence.orientation#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L858organon.charter.self-transcendence.non-finality#p1 sha256 4ae4497523e79e0606ab3849c47b6ea16f8888a952e063e6966eb36b750f3df8

Record source clause organon.charter.self-transcendence.non-finality#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L859organon.charter.self-transcendence.limits#p2 sha256 6dade83f0b7fcc004bdb37b6726c15b31b06a377de4e86d506c9d2e67847029d

Record source clause organon.charter.self-transcendence.limits#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L860organon.relationships.terms#p1 sha256 61cb7ce4f2920f1aa6771502b87a66536ae0504acccfebd9dd23bcc62756eddf

Record source clause organon.relationships.terms#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L861-/

Close the preceding source-mapping comment without adding a logical condition.

L862theorem generationCases :

Bundle checked generative valuation, permission-only failure, justified stability and real collaboration cases.

L863    (Generative openPolicy ∧

The explicitly open policy satisfies Generative.

L864    (∀ k : FormKind, openPolicy.revisable ⟨k, 0⟩) ∧

Additionally exposes revision permission for version zero of every form category.

L865    (∀ t, ¬ Expanded (stableTrace t) (stableTrace (t + 1)))) ∧

Every adjacent pair in the constant trace lacks a newly understood or constructed operation.

L866    (neutralPolicy.permitsVersion 0 1 ∧ (0 : Nat) ≠ 1 ∧ ¬ Generative neutralPolicy) ∧

States that neutralPolicy permits 0→1, the versions differ, and its missing valuation defeats Generative.

L867    (Generative generatingSystem.policy ∧

The concrete generating system's own policy satisfies Generative.

L868    generatingSystem.policy.permitsVersion 0 0 ∧

Its policy allows keeping version zero, so generativity does not require every action to change versions.

L869    ¬ Expanded generatingSystem.current inflatedState ∧

Inflating this system's inventory does not expand its represented capabilities.

L870    generatingSystem.current.inventory.length < inflatedState.inventory.length ∧

The inflated state has strictly more inventory entries than this system's current state.

L871    generatingSystem.current.abstractionLayers.length < inflatedState.abstractionLayers.length ∧

Its abstraction-layer count also strictly increases without capability expansion.

L872    generatingSystem.current.vocabulary.length < inflatedState.vocabulary.length ∧

Its vocabulary count strictly increases under the same unchanged capability content.

L873    generatingSystem.execute availableResources = some 6 ∧

With resources 1,2,3, this system's execution actually returns some 6.

L874    generatingSystem.execute { availableResources with experience := none } = none ∧

Removing experience from that same resource bundle makes the system's execution fail.

L875    generatingSystem.execute { availableResources with knowledge := none } = none ∧

Removing knowledge alone likewise makes its execution return none.

L876    generatingSystem.execute { availableResources with collaborator := none } = none ∧

Removing the collaborator input alone also makes execution fail.

L877    generatingSystem.execute ⟨none, none, none⟩ = none ∧

With all three external inputs absent, this same execution interface returns none.

L878    ¬ Expanded generatingSystem.current generatingSystem.stableAction ∧

The system's stable action yields no represented capability expansion.

L879    generatingSystem.stableAction = generatingSystem.current ∧

That stable action is exactly retention of the system's current state.

L880    generatingSystem.requirementsMet generatingSystem.stableAction ∧

Retention preserves the workload's required copy operation.

L881    generatingSystem.withinBudget generatingSystem.stableAction ∧

The retained one-item state fits this system's one-item application budget.

L882    ¬ generatingSystem.withinBudget inflatedState ∧

The duplicated inventory has two entries and exceeds this same system's one-item budget.

L883    StableReason generatingSystem.current inflatedState ∧

Stability has the stated reason: construction is unchanged, but only the current state fits the budget.

L884    (inflatedAnnouncement = generatingSystem.report inflatedState .successor 0 1 ∧

Identifies the report as this system's announcement about inflatedState, successor, input zero and output one.

L885      inflatedAnnouncement.owner = generatingSystem.owner ∧

The report's owner equals this generating system's owner.

L886      inflatedAnnouncement.before = generatingSystem.current ∧ inflatedAnnouncement.after = inflatedState ∧

The report uses this system's current state as baseline and inflatedState as result.

L887      inflatedAnnouncement.reportedNewOperation = .successor ∧

Confirms the alleged new operation is successor.

L888      inflatedAnnouncement.input = 0 ∧ inflatedAnnouncement.expectedOutput = 1 ∧

Confirms the announced test is input zero with expected output one.

L889      ¬ inflatedAnnouncement.claim ∧ ¬ Expanded inflatedAnnouncement.before inflatedAnnouncement.after)) ∧

States both that the announcement's substantive claim fails and that its own state pair has no expansion.

L890    (generationSpecification openPolicy ∧

The open policy satisfies the represented generation commitment.

L891    Expanded baseState (collaborativeRevision availableResources) ∧

The available collaborator yields a newly constructed or understood operation.

L892    ¬ Expanded baseState (collaborativeRevision { availableResources with collaborator := none }) ∧

Removing that same collaborator removes the represented expansion.

L893    assistedExecution ⟨none, none, none⟩ = none) :=

With no experience, knowledge or collaborator, assisted execution returns no result.

L894  ⟨revisionWithoutProgress, permissionNotValuation, generationLimits, collaborativeProgress⟩

Assemble the four actual component proofs into the full stated conjunction; their names alone are not evidence.

L896/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L897/-- organon-map CoreReader.Adopted.generationLimits012

Begin source-tracing metadata for CoreReader.Adopted.generationLimits012; this mapping is not a proof premise.

L898organon.charter.self-transcendence.orientation#p1 sha256 7f9b85c0816b3d69e417cf3cbe17b7b59931388f84d799ce6730c998037358bf

Record source clause organon.charter.self-transcendence.orientation#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L899organon.charter.self-transcendence.non-finality#p1 sha256 4ae4497523e79e0606ab3849c47b6ea16f8888a952e063e6966eb36b750f3df8

Record source clause organon.charter.self-transcendence.non-finality#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L900organon.charter.self-transcendence.limits#p1 sha256 6dade83f0b7fcc004bdb37b6726c15b31b06a377de4e86d506c9d2e67847029d

Record source clause organon.charter.self-transcendence.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L901organon.charter.self-transcendence.limits#p2 sha256 6dade83f0b7fcc004bdb37b6726c15b31b06a377de4e86d506c9d2e67847029d

Record source clause organon.charter.self-transcendence.limits#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L902organon.relationships.roles#p2 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L903-/

Close the preceding source-mapping comment without adding a logical condition.

L904theorem generationLimits012 :

Bundle generation's non-entailments: permission is not valuation, openness is not achievement, and content matters more than counts.

L905    (neutralPolicy.permitsVersion 0 1 ∧ (0 : Nat) ≠ 1 ∧ ¬ Generative neutralPolicy) ∧

States that neutralPolicy permits 0→1, the versions differ, and its missing valuation defeats Generative.

L906    (Generative openPolicy ∧

The open policy itself fulfills the valuation-and-revisability condition.

L907    (∀ k : FormKind, openPolicy.revisable ⟨k, 0⟩) ∧

Additionally exposes revision permission for version zero of every form category.

L908    (∀ t, ¬ Expanded (stableTrace t) (stableTrace (t + 1)))) ∧

Every adjacent pair in the constant trace lacks a newly understood or constructed operation.

L909    (Generative generatingSystem.policy ∧

The system is generative even in the following non-progress examples.

L910    generatingSystem.policy.permitsVersion 0 0 ∧

Its policy allows keeping version zero, so generativity does not require every action to change versions.

L911    ¬ Expanded generatingSystem.current inflatedState ∧

Inflating this system's inventory does not expand its represented capabilities.

L912    generatingSystem.current.inventory.length < inflatedState.inventory.length ∧

The inflated state has strictly more inventory entries than this system's current state.

L913    generatingSystem.current.abstractionLayers.length < inflatedState.abstractionLayers.length ∧

Its abstraction-layer count also strictly increases without capability expansion.

L914    generatingSystem.current.vocabulary.length < inflatedState.vocabulary.length ∧

Its vocabulary count strictly increases under the same unchanged capability content.

L915    generatingSystem.execute availableResources = some 6 ∧

With resources 1,2,3, this system's execution actually returns some 6.

L916    generatingSystem.execute { availableResources with experience := none } = none ∧

Removing experience from that same resource bundle makes the system's execution fail.

L917    generatingSystem.execute { availableResources with knowledge := none } = none ∧

Removing knowledge alone likewise makes its execution return none.

L918    generatingSystem.execute { availableResources with collaborator := none } = none ∧

Removing the collaborator input alone also makes execution fail.

L919    generatingSystem.execute ⟨none, none, none⟩ = none ∧

With all three external inputs absent, this same execution interface returns none.

L920    ¬ Expanded generatingSystem.current generatingSystem.stableAction ∧

The system's stable action yields no represented capability expansion.

L921    generatingSystem.stableAction = generatingSystem.current ∧

That stable action is exactly retention of the system's current state.

L922    generatingSystem.requirementsMet generatingSystem.stableAction ∧

Retention preserves the workload's required copy operation.

L923    generatingSystem.withinBudget generatingSystem.stableAction ∧

The retained one-item state fits this system's one-item application budget.

L924    ¬ generatingSystem.withinBudget inflatedState ∧

The duplicated inventory has two entries and exceeds this same system's one-item budget.

L925    StableReason generatingSystem.current inflatedState ∧

Stability has the stated reason: construction is unchanged, but only the current state fits the budget.

L926    (inflatedAnnouncement = generatingSystem.report inflatedState .successor 0 1 ∧

Identifies the report as this system's announcement about inflatedState, successor, input zero and output one.

L927      inflatedAnnouncement.owner = generatingSystem.owner ∧

The report's owner equals this generating system's owner.

L928      inflatedAnnouncement.before = generatingSystem.current ∧ inflatedAnnouncement.after = inflatedState ∧

The report uses this system's current state as baseline and inflatedState as result.

L929      inflatedAnnouncement.reportedNewOperation = .successor ∧

Confirms the alleged new operation is successor.

L930      inflatedAnnouncement.input = 0 ∧ inflatedAnnouncement.expectedOutput = 1 ∧

Confirms the announced test is input zero with expected output one.

L931      ¬ inflatedAnnouncement.claim ∧ ¬ Expanded inflatedAnnouncement.before inflatedAnnouncement.after)) ∧

States both that the announcement's substantive claim fails and that its own state pair has no expansion.

L932    (generationSpecification openPolicy ∧

The open policy satisfies the represented generation commitment.

L933    Expanded baseState (collaborativeRevision availableResources) ∧

The available collaborator yields a newly constructed or understood operation.

L934    ¬ Expanded baseState (collaborativeRevision { availableResources with collaborator := none }) ∧

Removing that same collaborator removes the represented expansion.

L935    assistedExecution ⟨none, none, none⟩ = none) ∧

With no experience, knowledge or collaborator, assisted execution returns no result.

L936    (Grounds012 transitionAchievement canonicalArticulation [transitionFacet] (taskOfFacet transitionFacet) ∧

The transition's performance facet fulfills the exact achievement task it declares.

L937    Compatible [transitionPerformanceRecord] .extend ∧

Require extend to satisfy the actual performance observation.

L938    transitionAchievement .extend ∧ ¬ transitionAchievement .inflate ∧

Extension adds capability; inventory inflation does not.

L939    ¬ Supports [transitionReportRecord] transitionAchievement) ∧

Conclude that the positive report records therefore do not support the achievement over all compatible transitions.

L940    (∀ kind : InventoryKind,

Quantify the inventory-content result over every represented item category.

L941    Available [⟨kind, .copy⟩, ⟨kind, .copy⟩] .copy ∧

Two copies of a copy item still provide the copy operation.

L942    ¬ Available [⟨kind, .copy⟩, ⟨kind, .copy⟩] .successor) :=

They do not provide the distinct successor operation.

L943  ⟨permissionNotValuation, revisionWithoutProgress, generationLimits, collaborativeProgress, achievementSupported012, inventoryCases012⟩

Combine six proofs, including actual collaborative progress, same-transition support and all-category duplication limits.

L945/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L946/-- organon-map CoreReader.Adopted.consistencyCases

Begin source-tracing metadata for CoreReader.Adopted.consistencyCases; this mapping is not a proof premise.

L947organon.charter.consistency#p1 sha256 c6960c590c096d33250599cf418e3c6a1dc26bfc7d7800c82b8efde656950f42

Record source clause organon.charter.consistency#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L948organon.charter.consistency.meaning#p1 sha256 81c09e38a3349499f95401d1c08f6069666c13547a43bc4e4395330743055faa

Record source clause organon.charter.consistency.meaning#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L949organon.charter.consistency.meaning#p2 sha256 81c09e38a3349499f95401d1c08f6069666c13547a43bc4e4395330743055faa

Record source clause organon.charter.consistency.meaning#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L950organon.charter.consistency.limits#p1 sha256 4fa1c29bf95ad6ef04c6d27671a832c0af8ba31b9c0d8018a8d09c4f33c38e75

Record source clause organon.charter.consistency.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L951-/

Close the preceding source-mapping comment without adding a logical condition.

L952theorem consistencyCases :

Bundle whole-set conflict, context distinctions, honest reporting, withdrawal and presentation-order cases.

L953    (Satisfiable (singleton premiseP) ∧ Satisfiable (singleton premiseRule) ∧

The first two conclusions provide separate models for P and its implication rule.

L954    Satisfiable (singleton premiseNotQ) ∧ ¬ Satisfiable jointTheory) ∧

Also require a separate model for not Q, but deny any model of the entire joint theory.

L955    ((Consequence emptyTheory (assumptionContext true) () true ∧

Require a positive answer under true-valued assumptions.

L956      Consequence emptyTheory (assumptionContext false) () false) ∧

Require the negative answer under false-valued assumptions; the contexts differ.

L957    (Consequence emptyTheory (meaningContext true) () true ∧

Require a positive answer for the question meaning equality to true.

L958      Consequence emptyTheory (meaningContext false) () false) ∧

Require the negative answer when that question instead means equality to false.

L959    (Consequence emptyTheory (scopeContext true) () true ∧

Require the positive answer in the scope restricted to true.

L960      Consequence emptyTheory (scopeContext false) () false) ∧

Require the negative answer in the different scope restricted to false.

L961    (∀ b, ∃ w, Admissible emptyTheory (assumptionContext b) w) ∧

For either assumption selector, require an actual admissible world.

L962    (∀ b, ∃ w, Admissible emptyTheory (meaningContext b) w) ∧

For either question meaning, require an actual admissible world.

L963    (∀ b, ∃ w, Admissible emptyTheory (scopeContext b) w)) ∧

For either scope selector, the conclusion includes an actual admissible world.

L964    (¬ TruthfulReport (contextSnapshot (assumptionContext true)) (contextSnapshot (assumptionContext false)) false ∧

Reject a false report when actual contextual assumptions change from true to false.

L965    ¬ TruthfulReport (contextSnapshot (meaningContext true)) (contextSnapshot (meaningContext false)) false ∧

Reject a false report when the question’s actual meaning changes.

L966    ¬ TruthfulReport (contextSnapshot (scopeContext true)) (contextSnapshot (scopeContext false)) false ∧

Reject a false report when the actual application scope changes.

L967    ¬ TruthfulReport (contextSnapshot (scopeContext true) 0) (contextSnapshot (scopeContext true) 1) false ∧

Reject a false report when revision identity changes from 0 to 1 despite unchanged context.

L968    (TruthfulReport (contextSnapshot (assumptionContext true)) (contextSnapshot (assumptionContext false)) true ∧

Permit truthful acknowledgement of the changed assumptions with a true report.

L969      ¬ Models (assumptionContext false).assumptions true)) ∧

Nevertheless deny that those revised false-world assumptions hold at actual true.

L970    (Satisfiable (revisionSlice 0) ∧ Satisfiable (revisionSlice 1) ∧

Require time slices 0 and 1 to have separate model witnesses.

L971    ¬ Satisfiable (union (revisionSlice 0) (revisionSlice 1))) ∧

Deny a model of their simultaneous union; this does not deny either separate witness.

L972    ((∀ time, Consistent (revisionSlice time) broadBoolContext) ∧

Quantify consistency over every current time slice.

L973    ¬ Consistent (union (revisionSlice 0) (revisionSlice 1)) broadBoolContext) ∧

Reject simultaneous retention of the opposing slices zero and one.

L974    (∀ p q : Claim Bool,

The ordering claim applies to arbitrary Boolean-world claims p and q.

L975    ∀ r, union (singleton p) (singleton q) r ↔ union (singleton q) (singleton p) r) ∧

Each member belongs to one singleton union exactly when it belongs to the reversed union.

L976    (Consequence jointTheory jointContext012 () true ∧

The joint theory implies the positive second-coordinate question.

L977    Consequence jointTheory jointContext012 () false ∧

It also implies that same question's negation in the same context.

L978    ¬ Consistent jointTheory jointContext012) :=

Therefore it violates the defined consistency condition.

L979  ⟨jointConflict, contextDifferences, hiddenContextChangeRejected, revisionCanReverse, sliceConsistency, semanticOrder012, jointImplicationConflict012⟩

Combine the seven checked components, retaining joint-implication conflict and separate-time consistency.

L981/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L982/-- organon-map CoreReader.Adopted.consistencyLimits012

Begin source-tracing metadata for CoreReader.Adopted.consistencyLimits012; this mapping is not a proof premise.

L983organon.charter.consistency.meaning#p2 sha256 81c09e38a3349499f95401d1c08f6069666c13547a43bc4e4395330743055faa

Record source clause organon.charter.consistency.meaning#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L984organon.charter.consistency.limits#p1 sha256 4fa1c29bf95ad6ef04c6d27671a832c0af8ba31b9c0d8018a8d09c4f33c38e75

Record source clause organon.charter.consistency.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L985organon.relationships.roles#p2 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L986-/

Close the preceding source-mapping comment without adding a logical condition.

L987theorem consistencyLimits012 :

Bundle consistency limits with actual context models, budget tension, false assumptions and lack of entailment.

L988    ((Consequence emptyTheory (assumptionContext true) () true ∧

Require a positive answer under true-valued assumptions.

L989      Consequence emptyTheory (assumptionContext false) () false) ∧

Require the negative answer under false-valued assumptions; the contexts differ.

L990    (Consequence emptyTheory (meaningContext true) () true ∧

Require a positive answer for the question meaning equality to true.

L991      Consequence emptyTheory (meaningContext false) () false) ∧

Require the negative answer when that question instead means equality to false.

L992    (Consequence emptyTheory (scopeContext true) () true ∧

Require the positive answer in the scope restricted to true.

L993      Consequence emptyTheory (scopeContext false) () false) ∧

Require the negative answer in the different scope restricted to false.

L994    (∀ b, ∃ w, Admissible emptyTheory (assumptionContext b) w) ∧

For either assumption selector, require an actual admissible world.

L995    (∀ b, ∃ w, Admissible emptyTheory (meaningContext b) w) ∧

For either question meaning, require an actual admissible world.

L996    (∀ b, ∃ w, Admissible emptyTheory (scopeContext b) w)) ∧

For either scope selector, the conclusion includes an actual admissible world.

L997    ((∃ budget : Nat, 4 ≤ budget ∧ budget ≤ 6) ∧

Ask for a natural-number budget satisfying both lower bound 4 and upper bound 6.

L998    ¬ ((fun n : Nat => 4 ≤ n) = (fun n : Nat => n ≤ 6))) ∧

Also assert that the two bound predicates are not identical, even though jointly satisfiable.

L999    (Consistent (singleton (fun w : Bool => w = true)) broadBoolContext ∧

The singleton on-theory is consistent in the broad context.

L1000    ¬ Models (singleton (fun w : Bool => w = true)) false ∧

Deny that actual false models the theory whose sole claim is world=true.

L1001    Consistent (emptyTheory : Theory Bool) broadBoolContext ∧

The empty held theory is also consistent in that context.

L1002    ¬ Entails emptyTheory (fun w : Bool => w = true)) ∧

The inhabited empty theory does not entail the positive true-world answer.

L1003    (Satisfiable (union emptyTheory (singleton (fun w : Bool => w = true))) ∧

Require a model where emptyTheory and the positive singleton claim hold together.

L1004    ¬ Entails emptyTheory (fun w : Bool => w = true)) ∧

The inhabited empty theory does not entail the positive true-world answer.

L1005    (Consistent (union (singleton (fun n : Nat => 4 ≤ n)) (singleton (fun n => n ≤ 6))) tensionContext012) :=

The whole held set requires 4≤n and n≤6 simultaneously.

L1006  ⟨contextDifferences, tensionWithoutContradiction, explicitlyConsistentLimits, compatibilityNotEntailment, tensionConsistent012⟩

Use all five component proofs; the last supplies a genuinely shared consistent allocation for both demands.

L1008/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1009/-- organon-map CoreReader.Adopted.reflexivityCases012

Begin source-tracing metadata for CoreReader.Adopted.reflexivityCases012; this mapping is not a proof premise.

L1010organon.charter.reflexivity#p1 sha256 13293b45c2fa89068c68ae7ef3c5df38f0efadb3ef3873d78a5ba67d9691a757

Record source clause organon.charter.reflexivity#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1011organon.charter.reflexivity.meaning#p1 sha256 8a2caede01a43d8b6c60b54c78ac089c51868e9956f316948077ccee2e45c9cc

Record source clause organon.charter.reflexivity.meaning#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1012organon.charter.reflexivity.limits#p1 sha256 ac0baae0d86e69f84c1ca4dee837de2759e2d29c295ffc257d988962158d4bbc

Record source clause organon.charter.reflexivity.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1013organon.relationships.roles#p3 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1014-/

Close the preceding source-mapping comment without adding a logical condition.

L1015theorem reflexivityCases012 :

Bundle applicable self-target work, Grounds self-assessment and its actual permission consequence.

L1016    (reflexivitySpecification ((ownRules 0).map legacyRule) (fun s => s.owner = 0)

The full registered own rules satisfy the generic reflexivity interface.

L1017      (legacyPerformed (ownRules 0) (completeOwnWork 0)) ∧

Their actual completed work supplies the performed applications.

L1018    (∀ phase, Performed (completeOwnWork 0) (.process 0 0 phase) .assessment) ∧

Assessment records exist for formation, application and revision phases.

L1019    Performed (completeOwnWork 0) (.system 0) .assessment ∧

There is also an actual system-self assessment.

L1020    reflexivitySpecification ([applicationRule].map legacyRule) (fun s => s.owner = 0)

A narrower application-only rule separately satisfies generic reflexivity.

L1021      (legacyPerformed [applicationRule] applicationWork) ∧

Its actual applicationWork is the source of performed work.

L1022    ¬ Performed applicationWork (.system 0) .assessment) ∧

Yet that same log contains no assessment of the system itself, where this rule is not applicable.

L1023    (Grounds012 (fun enabled => GroundsProvision012 enabled) canonicalArticulation [.value groundsPosition012] (.value groundsPosition012) ∧

The assessed claim is enforcement of Grounds, with the exact groundsPosition012 value task.

L1024    groundsPosition012.limits true ∧ groundsPosition012.relevantCriticism true) ∧

The adopted world lies in scope and has a live support-limit criticism.

L1025    (Compatible [zeroRecord] (localGenerator 0) ∧ ¬ allTrue (localGenerator 0) ∧

The same program matches the observed record and fails the global claim.

L1026    groundsExperiment012 true = false ∧ groundsExperiment012 false = true ∧

Enabled permission rejects that task; disabled permission accepts it.

L1027    groundsPosition012.outcome true true = groundsExperiment012 true ∧

The value position's enabled outcome is the actual enabled permission decision.

L1028    groundsPosition012.outcome true false = groundsExperiment012 false) :=

Its disabled outcome likewise is the actual disabled permission decision.

L1029  ⟨reflexiveTargets012, groundsOnGrounds012, groundsRationaleExperiment012⟩

Combine actual records with the checked value procedure and same-task enabled/disabled permission comparison.

L1031/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1032/-- organon-map CoreReader.Adopted.reflexivityLimits012

Begin source-tracing metadata for CoreReader.Adopted.reflexivityLimits012; this mapping is not a proof premise.

L1033organon.charter.reflexivity.limits#p1 sha256 ac0baae0d86e69f84c1ca4dee837de2759e2d29c295ffc257d988962158d4bbc

Record source clause organon.charter.reflexivity.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1034organon.relationships.roles#p3 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1035organon.relationships.roles#p1 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1036organon.grounds#p1 sha256 4ee74dc8617388ee75d63b507176ecb73b8527758b648f7c588d3ae7f3445ec6

Record source clause organon.grounds#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1037-/

Close the preceding source-mapping comment without adding a logical condition.

L1038theorem reflexivityLimits012 :

Bundle concrete failures of self-proof, self-origin support and self-exempt openness, including full Charter without the selected Grounds.

L1039    (selfTest [1] = true ∧ ownArithmeticPrinciple 0 = false ∧

The same arithmetic principle passes sample 1 but evaluates false at 0.

L1040      ¬ (∀ n, ownArithmeticPrinciple n = true)) ∧

Therefore that principle does not return true for every natural-number input.

L1041    (localGenerator 0 0 = true ∧ localGenerator 0 1 = false ∧

Compute localGenerator 0 as true at 0 and false at 1.

L1042    Compatible [zeroRecord] (localGenerator 0) ∧

Require this generated function to match the same input-0 record.

L1043    ¬ Supports [zeroRecord] allTrue ∧ OwnedRevisionExample) ∧

State failure of all-input support and include the concrete owner/prior/revision relationship example.

L1044    (Generative openPolicy ∧ ¬ Reflexive 0 (ownRules 0) []) ∧

Combines a generative openPolicy with failure of owned reflexivity when the work log is empty.

L1045    (CompleteCharter012 CoreReader.Integration.actualSystem CoreReader.Integration.actual ∧

The very concrete system/world fulfills every represented Charter component.

L1046    Admissible CoreReader.Integration.held CoreReader.Integration.context CoreReader.Integration.actual ∧

It also supplies an actual admissible world for the held theory and context.

L1047    Compatible [CoreReader.Integration.costAllowanceRecord] CoreReader.Integration.actual ∧

The concrete cost-allowance record is true in that world.

L1048    Articulated (canonicalArticulation CoreReader.Integration.unsupportedCapabilityFacet) ∧

The proposed capability facet has identifiable canonical articulation.

L1049    ¬ Supports [CoreReader.Integration.costAllowanceRecord] CoreReader.Integration.capability ∧

That true cost record cannot support the actual output capability.

L1050    ¬ Grounds012 CoreReader.Integration.capability canonicalArticulation

Consequently the same capability fails Grounds with these proposed grounds.

L1051      [CoreReader.Integration.unsupportedCapabilityFacet]

The candidate list contains the identified unsupported capability facet.

L1052      (taskOfFacet CoreReader.Integration.unsupportedCapabilityFacet)) ∧

Its original task retains that facet's empirical claim and support context.

L1053    (generationSpecification openPolicy ∧ openPolicy.revisable ⟨.principle,0⟩ ∧

The policy values expansion and keeps the principle form revisable.

L1054    selfExemptPerformed012 ⟨0,1⟩ 1 1 true ∧

An actual assessment of target one returns true.

L1055    selfExemptRule012.applicable 0 ∧

Nevertheless the same rule is applicable to self-target zero.

L1056    ¬ reflexivitySpecification [selfExemptRule012] (fun target => target = 0) selfExemptPerformed012) :=

It fails reflexivity because that applicable self-target receives no work.

L1057  ⟨selfTestDoesNotProve, selfOriginDoesNotSupport, generationNotReflexivity, charterWithoutGrounds012, openSelfExempt012⟩

Use five concrete component proofs rather than inferring correctness from self-application.

L1059/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1060/-- organon-map CoreReader.Adopted.groundsCases012

Begin source-tracing metadata for CoreReader.Adopted.groundsCases012; this mapping is not a proof premise.

L1061organon.grounds#p1 sha256 4ee74dc8617388ee75d63b507176ecb73b8527758b648f7c588d3ae7f3445ec6

Record source clause organon.grounds#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1062organon.grounds.assessment#p1 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1063organon.grounds.assessment#p2 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1064organon.grounds.assessment#p3 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1065-/

Close the preceding source-mapping comment without adding a logical condition.

L1066theorem groundsCases012 :

Bundle same-task Grounds examples and the rejected circular-assumption substitution.

L1067    (Grounds012 localFacet012.claim canonicalArticulation [localFacet012] (taskOfFacet localFacet012) ∧

The local claim fulfills its explicitly declared local task.

L1068    Articulated (canonicalArticulation globalFacet012) ∧

The global candidate is nevertheless clearly articulated.

L1069    ¬ Grounds012 globalFacet012.claim canonicalArticulation [globalFacet012] (taskOfFacet globalFacet012) ∧

The all-input task fails Grounds despite that articulation.

L1070    ¬ Grounds012 strongFacet012.claim canonicalArticulation [strongFacet012] (taskOfFacet strongFacet012)) ∧

The two-output task also fails with the same records.

L1071    (Articulated uninformativeArgument ∧

The uninformative argument still has identifiable concepts and reasons.

L1072    ¬ Entails uninformativeArgument.assumptions (fun w : Bool => w = true)) ∧

The uninformative articulation’s actual assumptions do not entail that the world is true.

L1073    (Grounds012 allTrue canonicalArticulation [circularGlobalFacet012] (taskOfFacet circularGlobalFacet012) ∧

The circular facet has Grounds for its own explicitly new conditional task.

L1074    ¬ NatureAppropriate originalGlobalTask012 circularGlobalFacet012 ∧

It is not appropriate to the previously fixed global empirical task.

L1075    ¬ Grounds012 allTrue canonicalArticulation [circularGlobalFacet012] originalGlobalTask012) :=

Thus it cannot fulfill that original task merely by sharing its conclusion.

L1076  ⟨scopeStrength012, articulationNotSupport, circularSubstitutionRejected012⟩

Combine scope/strength countermodels, articulation without support, and preserved-original-task rejection.

L1078/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1079/-- organon-map CoreReader.Adopted.empiricalCases012

Begin source-tracing metadata for CoreReader.Adopted.empiricalCases012; this mapping is not a proof premise.

L1080organon.grounds.assessment#p2 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1081-/

Close the preceding source-mapping comment without adding a logical condition.

L1082theorem empiricalCases012 :

Bundle empirical relevance, scope, uncertainty and alternative-assessment cases with original tasks preserved.

L1083    (Grounds012 localFacet012.claim canonicalArticulation [localFacet012] (taskOfFacet localFacet012) ∧

The local claim fulfills its explicitly declared local task.

L1084    Articulated (canonicalArticulation globalFacet012) ∧

The global candidate is nevertheless clearly articulated.

L1085    ¬ Grounds012 globalFacet012.claim canonicalArticulation [globalFacet012] (taskOfFacet globalFacet012) ∧

The all-input task fails Grounds despite that articulation.

L1086    ¬ Grounds012 strongFacet012.claim canonicalArticulation [strongFacet012] (taskOfFacet strongFacet012)) ∧

The two-output task also fails with the same records.

L1087    (temperatureRecord.test (true,false) = true ∧

The actual temperature test returns true even when the independent output coordinate is false.

L1088    Compatible [temperatureRecord,temperatureRecord] (true,false) ∧

Retain this false-output world under repeated temperature observations.

L1089    Compatible [temperatureRecord,temperatureRecord] (true,true) ∧

Also retain a true-output world under those same repeated observations.

L1090    ¬ Supports [temperatureRecord] (fun w : Bool × Bool => w.2 = true) ∧

A single temperature record does not support the other output being true.

L1091    ¬ Supports [temperatureRecord,temperatureRecord] (fun w : Bool × Bool => w.2 = true) ∧

Repeating that temperature record still does not support the other output being true.

L1092    Compatible [actionRecord,actionRecord] (true,0) ∧

Repeated observed activation is compatible with selected-on and budget 0.

L1093    Compatible [actionRecord,actionRecord] (true,3) ∧

The same repeated records are also compatible with budget 3.

L1094    ¬ Supports [actionRecord] announcementPosition.consequence ∧

A single activation record does not support the option’s actual objective-and-budget consequence.

L1095    ¬ Supports [actionRecord,actionRecord] announcementPosition.consequence ∧

Repeating activation records does not repair that lack of consequence support.

L1096    ¬ ValueProcedure announcementPosition) ∧

The announcement-based value procedure also fails for that actual option and constraint.

L1097    (empiricalSpecification [temperatureRecord, temperatureRecord] (fun _ => True)

The empirical task uses the same repeated temperature records.

L1098      (fun w => w.1 = true) (fun w => w.2 = true ∨ w.2 = false) ∧

The claim fixes only coordinate one; uncertainty explicitly allows coordinate two to vary.

L1099    Compatible [temperatureRecord, temperatureRecord] (true,true) ∧

The true/true world matches the repeated records.

L1100    Compatible [temperatureRecord, temperatureRecord] (true,false)) ∧

The true/false world matches them as well.

L1101    (Grounds012 (fun f => f 0 = true) canonicalArticulation [localFacet012] originalLocalTask012 ∧

The original empirical facet fulfills the fixed local task.

L1102    Grounds012 (fun f => f 0 = true) canonicalArticulation [observedInferenceFacet012] originalLocalTask012) ∧

The legitimate observation-based inference fulfills that very same task.

L1103    (FacetDischarged uncertaintyBypassFacet012 ∧

Retain the valid candidate's own discharge.

L1104    ¬ NatureAppropriate originalUncertaintyTask012 uncertaintyBypassFacet012 ∧

Reject its appropriateness to the full original uncertainty task.

L1105    ¬ Grounds012 (fun w : Bool × Bool => w.1 = true) canonicalArticulation

Reject Grounds for this original first-coordinate assertion and its unchanged articulation.

L1106      [uncertaintyBypassFacet012] originalUncertaintyTask012) :=

The candidate must still be checked against the full original uncertainty task.

L1107  ⟨scopeStrength012, measurementRepeatNotSupport, uncertainSupported012, sameEmpiricalTaskTwoMethods012, uncertaintySubstitutionRejected012⟩

Use all five component proofs, including legitimate empirical-to-inference assessment and the rejected uncertainty bypass.

L1109/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1110/-- organon-map CoreReader.Adopted.inferentialCases012

Begin source-tracing metadata for CoreReader.Adopted.inferentialCases012; this mapping is not a proof premise.

L1111organon.grounds.assessment#p2 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1112organon.relationships.roles#p2 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1113-/

Close the preceding source-mapping comment without adding a logical condition.

L1114theorem inferentialCases012 :

Bundle valid inference, compatible-but-unentailed conclusions and rejected changes of original premises.

L1115    (inferentialSpecification (singleton (fun n : Nat => n = 2)) (fun n => n + 1 = 3) ∧

From the stated assumption n=2 the scoped inference establishes n+1=3.

L1116    InferenceExamined (emptyTheory : Theory Bool) (fun w => w = true) false ∧

The empty Boolean theory accurately receives a negative report for the on-claim.

L1117    Models (emptyTheory : Theory Bool) false ∧ ¬ ((fun w : Bool => w = true) false)) ∧

The false world satisfies the same empty premises while falsifying that conclusion.

L1118    (Satisfiable (union emptyTheory (singleton (fun w : Bool => w = true))) ∧

Require a model where emptyTheory and the positive singleton claim hold together.

L1119    ¬ Entails emptyTheory (fun w : Bool => w = true)) ∧

The inhabited empty theory does not entail the positive true-world answer.

L1120    (FacetDischarged (Facet.inferential (singleton (fun w : Bool => w = true)) (fun w => w = true)) ∧

Include an inferential facet whose satisfiable true-world premise entails the same true-world claim.

L1121    ¬ Grounds012 (fun w : Bool => w = true) canonicalArticulation

Reject Grounds for the original on-claim when the inference context has been substituted.

L1122      [.inferential (singleton (fun w => w = true)) (fun w => w = true)]

The proposed candidate assumes the conclusion itself as its premise.

L1123      (.inferential emptyTheory (fun w => w = true))) :=

The fixed original task instead contains an empty assumption theory.

L1124  ⟨inferenceChecked012, compatibilityNotEntailment, inferentialContextSubstitutionRejected012⟩

Combine the arithmetic/negative-report proof, actual countervaluation and original-context substitution rejection.

L1126/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1127/-- organon-map CoreReader.Adopted.valueCases012

Begin source-tracing metadata for CoreReader.Adopted.valueCases012; this mapping is not a proof premise.

L1128organon.grounds.assessment#p2 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1129organon.grounds.assessment#p3 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1130-/

Close the preceding source-mapping comment without adding a logical condition.

L1131theorem valueCases012 :

Bundle reasoned value adoption, insufficient self-announcement, live criticism, initial commitments and fact/value distinction.

L1132    (valueSpecification switchPosition) ∧

The switch value task has its own fulfilled reasons and responsibilities.

L1133    (announcementPosition.reasons ≠ [] ∧ announcementPosition.commitment (true,0) ∧

Require nonempty announcement reasons and actual adoption at selected-on with budget 0.

L1134    (∀ reason, reason ∈ announcementPosition.reasons → reason (true,0) announcementPosition.adopted) ∧

At that same zero-budget world, all actual announcement reasons hold.

L1135    ¬ announcementPosition.consequence (true,0) ∧ ¬ ValueProcedure announcementPosition) ∧

Nevertheless reject the actual consequence and the whole value procedure.

L1136    (¬ ValueProcedure closedPosition012) ∧

Closing every criticism response makes closedPosition012 fail the value procedure.

L1137    (ValueProcedure switchPosition ∧

The original switch position does satisfy the represented value procedure.

L1138    Satisfiable switchPosition.starting ∧

Its explicitly adopted starting assumptions have a real model.

L1139    ¬ Entails (emptyTheory : Theory Bool) switchPosition.commitment ∧

Deny derivation of its adopted commitment from the empty Boolean theory.

L1140    (JointAdoption oppositePosition ∧ ¬ ValueProcedure oppositePosition) ∧

The opposite position has a joint witness but fails consequence assessment.

L1141    (¬ ValueProcedure contradictoryStartingPosition ∧ ¬ ValueProcedure impossibleAdoptionPosition)) ∧

Reject the procedures for contradictory starting assumptions and impossible actual adoption separately.

L1142    (FacetDischarged selectedFactFacet012 ∧ valueSpecification switchPosition ∧

The empirical selection facet is discharged and the reasoned value position independently fulfills its task.

L1143    ¬ Grounds012 switchPosition.commitment canonicalArticulation [selectedFactFacet012] (.value switchPosition)) :=

The empirical fact alone nevertheless cannot fulfill the fixed value-position task.

L1144  ⟨valueFulfilled012, announcementNotBudgetReason, closedCriticism012, valueWithoutSelfProof, valueFactSubstitutionRejected012⟩

Assemble the five value proofs while retaining assumptions, limits and actual negative cases.

L1146/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1147/-- organon-map CoreReader.Adopted.groundsLimits012

Begin source-tracing metadata for CoreReader.Adopted.groundsLimits012; this mapping is not a proof premise.

L1148organon.grounds.assessment#p1 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1149organon.grounds.assessment#p2 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1150organon.grounds.assessment#p3 sha256 ac2f84ce07036731964e26221e6d3ef83c9b647ebe249862eb2bc115856e6e4d

Record source clause organon.grounds.assessment#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1151-/

Close the preceding source-mapping comment without adding a logical condition.

L1152theorem groundsLimits012 :

Bundle limits on clear reasons, repeated irrelevant facts, self-proof demands and numerical commensurability.

L1153    (Articulated clearFalseArgument012 ∧ ¬ Models clearFalseArgument012.assumptions false) ∧

Its fields are identifiable, but the false world does not model its assumptions.

L1154    (temperatureRecord.test (true,false) = true ∧

The actual temperature test returns true even when the independent output coordinate is false.

L1155    Compatible [temperatureRecord,temperatureRecord] (true,false) ∧

Retain this false-output world under repeated temperature observations.

L1156    Compatible [temperatureRecord,temperatureRecord] (true,true) ∧

Also retain a true-output world under those same repeated observations.

L1157    ¬ Supports [temperatureRecord] (fun w : Bool × Bool => w.2 = true) ∧

A single temperature record does not support the other output being true.

L1158    ¬ Supports [temperatureRecord,temperatureRecord] (fun w : Bool × Bool => w.2 = true) ∧

Repeating that temperature record still does not support the other output being true.

L1159    Compatible [actionRecord,actionRecord] (true,0) ∧

Repeated observed activation is compatible with selected-on and budget 0.

L1160    Compatible [actionRecord,actionRecord] (true,3) ∧

The same repeated records are also compatible with budget 3.

L1161    ¬ Supports [actionRecord] announcementPosition.consequence ∧

A single activation record does not support the option’s actual objective-and-budget consequence.

L1162    ¬ Supports [actionRecord,actionRecord] announcementPosition.consequence ∧

Repeating activation records does not repair that lack of consequence support.

L1163    ¬ ValueProcedure announcementPosition) ∧

The announcement-based value procedure also fails for that actual option and constraint.

L1164    (valueSpecification switchPosition ∧

The switch value task has its own fulfilled reasons and responsibilities.

L1165    Compatible [valueNeutralRecord012] false ∧

The opposite selection false is compatible with the neutral record.

L1166    ¬ Supports [valueNeutralRecord012] switchPosition.commitment ∧

Thus those records do not establish adoption of the switch commitment.

L1167    ¬ Entails (emptyTheory : Theory Bool) switchPosition.commitment) ∧

Deny derivation of its adopted commitment from the empty Boolean theory.

L1168    (ValueProcedure switchPosition ∧

The finite switch value procedure is fulfilled in its stated interpretation.

L1169    Satisfiable switchPosition.starting ∧

The adopted starting theory is satisfiable, without claiming it follows from empty facts.

L1170    ¬ Entails (emptyTheory : Theory Bool) switchPosition.commitment ∧

Deny derivation of its adopted commitment from the empty Boolean theory.

L1171    (JointAdoption oppositePosition ∧ ¬ ValueProcedure oppositePosition) ∧

The opposite position has a joint witness but fails consequence assessment.

L1172    (¬ ValueProcedure contradictoryStartingPosition ∧ ¬ ValueProcedure impossibleAdoptionPosition)) ∧

Reject the procedures for contradictory starting assumptions and impossible actual adoption separately.

L1173    (ClaimNoStronger (fun f : Nat → Bool => f 0 = true) allTrue ∧

Truth at every input implies truth at input zero.

L1174    ¬ ClaimNoStronger allTrue (fun f : Nat → Bool => f 0 = true) ∧

Truth at zero does not imply truth at every input.

L1175    valueSpecification switchPosition) :=

The switch value task has its own fulfilled reasons and responsibilities.

L1176  ⟨clearFalseReason012, measurementRepeatNotSupport, valueNotFact012, valueWithoutSelfProof, qualitativeProportionality012⟩

Combine concrete false-reason and wrong-object counterexamples with the value and qualitative-strength results.

L1178/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1179/-- organon-map CoreReader.Adopted.scopeCases012

Begin source-tracing metadata for CoreReader.Adopted.scopeCases012; this mapping is not a proof premise.

L1180organon.grounds.scope#p1 sha256 4a0e93c7834e4ef62f129ee4621cf7bf1c93b64d86f9f145d1592adcf9fb6693

Record source clause organon.grounds.scope#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1181organon.grounds.scope#p2 sha256 4a0e93c7834e4ef62f129ee4621cf7bf1c93b64d86f9f145d1592adcf9fb6693

Record source clause organon.grounds.scope#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1182organon.grounds.scope#p3 sha256 4a0e93c7834e4ef62f129ee4621cf7bf1c93b64d86f9f145d1592adcf9fb6693

Record source clause organon.grounds.scope#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1183-/

Close the preceding source-mapping comment without adding a logical condition.

L1184theorem scopeCases012 :

Bundle a fulfilled local scope account with an actual omitted difference.

L1185    (scopeSpecification localScopeAccount012) ∧

The defined local account satisfies every represented comparison and method-role duty.

L1186    ((∀ n : Nat, n = 0 → (fun _ : Nat => true) n = localGenerator 0 n) ∧

State equality of both functions only for inputs satisfying n=0.

L1187    (fun _ : Nat => true) 1 ≠ localGenerator 0 1) :=

State their concrete output inequality at input 1.

L1188  ⟨scopeFulfilled012, hiddenDifference⟩

Use the actual scope-account proof and the input-one difference witness.

L1190/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1191/-- organon-map CoreReader.Adopted.scopeLimits012

Begin source-tracing metadata for CoreReader.Adopted.scopeLimits012; this mapping is not a proof premise.

L1192organon.grounds.scope#p1 sha256 4a0e93c7834e4ef62f129ee4621cf7bf1c93b64d86f9f145d1592adcf9fb6693

Record source clause organon.grounds.scope#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1193organon.grounds.scope#p2 sha256 4a0e93c7834e4ef62f129ee4621cf7bf1c93b64d86f9f145d1592adcf9fb6693

Record source clause organon.grounds.scope#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1194organon.grounds.scope#p3 sha256 4a0e93c7834e4ef62f129ee4621cf7bf1c93b64d86f9f145d1592adcf9fb6693

Record source clause organon.grounds.scope#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1195organon.grounds.implementations.limits#p1 sha256 db9b5f1803baab0e1b05a3a9e068948667412afa7d692e1da3869ca54be4b870

Record source clause organon.grounds.implementations.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1196-/

Close the preceding source-mapping comment without adding a logical condition.

L1197theorem scopeLimits012 :

Bundle limited local support, broader differences, trial distinctions and nonobservational assessment.

L1198    ((∃ outside : Nat, outside ≠ 0) ∧

There is an actual natural input outside the observed zero input.

L1199    Compatible [zeroRecord] (fun _ => true) ∧

The constant-true function matches the zero observation.

L1200    Compatible [zeroRecord] (localGenerator 0) ∧

Require this generated function to match the same input-0 record.

L1201    allTrue (fun _ => true) ∧ ¬ allTrue (localGenerator 0) ∧

The first function is universally true while the second is not.

L1202    ¬ Supports [zeroRecord] allTrue) ∧

The original zero record does not support all-input truth.

L1203    ((∀ n : Nat, n = 0 → (fun _ : Nat => true) n = localGenerator 0 n) ∧

State equality of both functions only for inputs satisfying n=0.

L1204    (fun _ : Nat => true) 1 ≠ localGenerator 0 1) ∧

State their concrete output inequality at input 1.

L1205    ([zeroRecord].length = 1 ∧

The evidence list contains exactly one observation.

L1206    (∃ f, Compatible [zeroRecord] f) ∧

That single observation has a real compatible function, so the support example is nonempty.

L1207    Supports [zeroRecord] (fun f => f 0 = true) ∧

That single record supports its actual input-0 claim.

L1208    ¬ Supports [zeroRecord] allTrue) ∧

Its limited support still does not establish allTrue.

L1209    (let a : Trial := ⟨0,1,1⟩

Define trial a with setting zero and an accurately recorded actual outcome one.

L1210    let b : Trial := ⟨0,2,2⟩

Define trial b at the same setting with accurately recorded actual outcome two.

L1211    Reproduced a b ∧ a.actualOutcome ≠ b.actualOutcome ∧ Bounded a ∧ Bounded b) ∧

Require the two explicitly fixed trials to share settings, differ in actual outcomes and both satisfy actualOutcome ≤ 2.

L1212    ((Verified ⟨0,1,1⟩ ∧ Verified ⟨1,1,1⟩ ∧ ¬ Reproduced ⟨0,1,1⟩ ⟨1,1,1⟩) ∧

Require two accurately recorded trials whose settings nevertheless differ.

L1213    (Reproduced ⟨0,1,1⟩ ⟨0,3,2⟩ ∧ ¬ Verified ⟨0,3,2⟩ ∧ ¬ Bounded ⟨0,3,2⟩) ∧

Require repeated settings alongside an inaccurate second record and an actual result exceeding the bound.

L1214    (Bounded ⟨0,1,1⟩ ∧ Bounded ⟨0,2,0⟩ ∧ ¬ Verified ⟨0,2,0⟩)) ∧

Require preserved bounds even though one recorded outcome is inaccurate.

L1215    (FacetDischarged arithmeticFacet ∧ usesObservation arithmeticFacet = false) ∧

The arithmetic facet is discharged although its method uses no observation.

L1216    (inferentialSpecification (singleton (fun on : Bool => on = true)) (fun on => on ≠ false) ∧

Under the explicit premise on=true, infer on≠false.

L1217    usesObservation (Facet.inferential (singleton (fun on : Bool => on = true)) (fun on => on ≠ false)) = false) ∧

The actual inferential facet reports that it does not use observation.

L1218    (drawWeight012 true > 0 ∧ drawWeight012 false > 0 ∧

Both possible draw weights are positive.

L1219    drawWeight012 true = drawWeight012 false ∧

The two weights are equal.

L1220    Reproduced (randomTrial012 true) (randomTrial012 false) ∧

Both trials reproduce the same setting.

L1221    (randomTrial012 true).actualOutcome ≠ (randomTrial012 false).actualOutcome ∧

Their actual outcomes nevertheless differ.

L1222    (∀ draw, Verified (randomTrial012 draw) ∧ Bounded (randomTrial012 draw))) :=

For every draw the record is accurate and the actual outcome is at most two.

L1223  ⟨localNotUniversal, hiddenDifference, singleObservation, variableOutcomesStableBound, verificationReproductionStability, noUniversalChain, qualitativeUnmeasured012, randomOutcomes012⟩

Combine eight proofs; finite weighted draws and logical decisions are not claimed as empirical universal guarantees.

L1225/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1226/-- organon-map CoreReader.Adopted.capabilityCases012

Begin source-tracing metadata for CoreReader.Adopted.capabilityCases012; this mapping is not a proof premise.

L1227organon.grounds.capabilities#p1 sha256 7249f6f2ef327baaa72349cae53b9245f23a34436356dd05f3c6005cab35e8f0

Record source clause organon.grounds.capabilities#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1228organon.grounds.capabilities#p2 sha256 7249f6f2ef327baaa72349cae53b9245f23a34436356dd05f3c6005cab35e8f0

Record source clause organon.grounds.capabilities#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1229organon.relationships.roles#p2 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1230organon.relationships.roles#p3 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1231-/

Close the preceding source-mapping comment without adding a logical condition.

L1232theorem capabilityCases012 :

Bundle exact-object output and explanation contracts with the same duty for an owner's own claim.

L1233    (capabilitySpecification outputOnlyProcess OutputContract ∧

The output-only process has Grounds for its output contract.

L1234    capabilitySpecification explainedProcess FullProcessContract ∧

The explained process has Grounds for the stronger output-plus-explanation contract.

L1235    (∃ certificate : ExternalCertificate outputOnlyProcess,

Require an actual external certificate indexed by outputOnlyProcess.

L1236      certificate.assessorId ≠ certificate.assessedId ∧ OutputContract outputOnlyProcess) ∧

Require their distinction and actual output correctness of the same process.

L1237    ¬ ExplanationContract outputOnlyProcess) ∧

Still deny an internal explanation contract for that actual process.

L1238    (OwnCapability012 7 7 outputOnlyProcess OutputContract) ∧

Retain the existing own-capability case and conjoin the additional understanding cases.

L1239    (explainedWithoutVariation012.process = mechanismResponder012.process ∧

Both application objects contain exactly the same original process, so their outputs and explanation are identical.

L1240    FullProcessContract explainedWithoutVariation012.process ∧

The object with wrong variation answers still satisfies the original output-and-explanation contract.

L1241    ¬ UnderstandingApplication012 explainedWithoutVariation012 ∧

That object fails the stronger application understanding task.

L1242    UnderstandingApplication012 mechanismResponder012 ∧

The mechanism responder satisfies that stronger task.

L1243    Grounds012 UnderstandingApplication012 canonicalArticulation

Assert Grounds for the exact stronger understanding claim using canonical articulation.

L1244      [understandingFacet012 mechanismResponder012] (understandingTask012 mechanismResponder012) ∧

The positive facet and the fixed original task both identify the mechanism responder.

L1245    ¬ Grounds012 UnderstandingApplication012 canonicalArticulation

Deny Grounds for the same stronger understanding claim in the negative object case.

L1246      [understandingFacet012 explainedWithoutVariation012] (understandingTask012 explainedWithoutVariation012)) :=

The negative assessment retains that object's own fixed task and identity scope, closing the additional understanding cases.

L1247  ⟨capabilityFulfilled012, ownCapability012, understandingApplicationCases012⟩

Construct the bundle from the preserved capability and own-capability proofs and the new understanding-case proof.

L1249/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1250/-- organon-map CoreReader.Adopted.capabilityLimits012

Begin source-tracing metadata for CoreReader.Adopted.capabilityLimits012; this mapping is not a proof premise.

L1251organon.grounds.capabilities#p1 sha256 7249f6f2ef327baaa72349cae53b9245f23a34436356dd05f3c6005cab35e8f0

Record source clause organon.grounds.capabilities#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1252organon.grounds.capabilities#p2 sha256 7249f6f2ef327baaa72349cae53b9245f23a34436356dd05f3c6005cab35e8f0

Record source clause organon.grounds.capabilities#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1253-/

Close the preceding source-mapping comment without adding a logical condition.

L1254theorem capabilityLimits012 :

Bundle reliable output without explanation and inventory/resource limits on stronger capability claims.

L1255    (capabilitySpecification outputOnlyProcess OutputContract ∧

The output-only process has Grounds for its output contract.

L1256    capabilitySpecification explainedProcess FullProcessContract ∧

The explained process has Grounds for the stronger output-plus-explanation contract.

L1257    (∃ certificate : ExternalCertificate outputOnlyProcess,

Require an actual external certificate indexed by outputOnlyProcess.

L1258      certificate.assessorId ≠ certificate.assessedId ∧ OutputContract outputOnlyProcess) ∧

Require their distinction and actual output correctness of the same process.

L1259    ¬ ExplanationContract outputOnlyProcess) ∧

Still deny an internal explanation contract for that actual process.

L1260    (∀ kind : InventoryKind,

The duplication claim applies to each represented inventory kind.

L1261    Available [⟨kind, .copy⟩, ⟨kind, .copy⟩] .copy ∧

Two copies of a copy item still provide the copy operation.

L1262    ¬ Available [⟨kind, .copy⟩, ⟨kind, .copy⟩] .successor) ∧

They do not provide the distinct successor operation.

L1263    (Generative generatingSystem.policy ∧

The same concrete generating system has a generative policy.

L1264    generatingSystem.policy.permitsVersion 0 0 ∧

Its policy allows keeping version zero, so generativity does not require every action to change versions.

L1265    ¬ Expanded generatingSystem.current inflatedState ∧

Inflating this system's inventory does not expand its represented capabilities.

L1266    generatingSystem.current.inventory.length < inflatedState.inventory.length ∧

The inflated state has strictly more inventory entries than this system's current state.

L1267    generatingSystem.current.abstractionLayers.length < inflatedState.abstractionLayers.length ∧

Its abstraction-layer count also strictly increases without capability expansion.

L1268    generatingSystem.current.vocabulary.length < inflatedState.vocabulary.length ∧

Its vocabulary count strictly increases under the same unchanged capability content.

L1269    generatingSystem.execute availableResources = some 6 ∧

With resources 1,2,3, this system's execution actually returns some 6.

L1270    generatingSystem.execute { availableResources with experience := none } = none ∧

Removing experience from that same resource bundle makes the system's execution fail.

L1271    generatingSystem.execute { availableResources with knowledge := none } = none ∧

Removing knowledge alone likewise makes its execution return none.

L1272    generatingSystem.execute { availableResources with collaborator := none } = none ∧

Removing the collaborator input alone also makes execution fail.

L1273    generatingSystem.execute ⟨none, none, none⟩ = none ∧

With all three external inputs absent, this same execution interface returns none.

L1274    ¬ Expanded generatingSystem.current generatingSystem.stableAction ∧

The system's stable action yields no represented capability expansion.

L1275    generatingSystem.stableAction = generatingSystem.current ∧

That stable action is exactly retention of the system's current state.

L1276    generatingSystem.requirementsMet generatingSystem.stableAction ∧

Retention preserves the workload's required copy operation.

L1277    generatingSystem.withinBudget generatingSystem.stableAction ∧

The retained one-item state fits this system's one-item application budget.

L1278    ¬ generatingSystem.withinBudget inflatedState ∧

The duplicated inventory has two entries and exceeds this same system's one-item budget.

L1279    StableReason generatingSystem.current inflatedState ∧

Stability has the stated reason: construction is unchanged, but only the current state fits the budget.

L1280    (inflatedAnnouncement = generatingSystem.report inflatedState .successor 0 1 ∧

Identifies the report as this system's announcement about inflatedState, successor, input zero and output one.

L1281      inflatedAnnouncement.owner = generatingSystem.owner ∧

The report's owner equals this generating system's owner.

L1282      inflatedAnnouncement.before = generatingSystem.current ∧ inflatedAnnouncement.after = inflatedState ∧

The report uses this system's current state as baseline and inflatedState as result.

L1283      inflatedAnnouncement.reportedNewOperation = .successor ∧

Confirms the alleged new operation is successor.

L1284      inflatedAnnouncement.input = 0 ∧ inflatedAnnouncement.expectedOutput = 1 ∧

Confirms the announced test is input zero with expected output one.

L1285      ¬ inflatedAnnouncement.claim ∧ ¬ Expanded inflatedAnnouncement.before inflatedAnnouncement.after)) :=

States both that the announcement's substantive claim fails and that its own state pair has no expansion.

L1286  ⟨capabilityFulfilled012, inventoryCases012, generationLimits⟩

Combine scoped capability proofs, all-category content checks and actual generation/resource limits.

L1288/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1289/-- organon-map CoreReader.Adopted.choiceCases012

Begin source-tracing metadata for CoreReader.Adopted.choiceCases012; this mapping is not a proof premise.

L1290organon.grounds.implementations#p1 sha256 bb2a822a304d4a20f513218f356ddbeeca8ee139e3ed802213591e9ff6c5095c

Record source clause organon.grounds.implementations#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1291organon.grounds.implementations#p2 sha256 bb2a822a304d4a20f513218f356ddbeeca8ee139e3ed802213591e9ff6c5095c

Record source clause organon.grounds.implementations#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1292organon.grounds.implementations.limits#p1 sha256 db9b5f1803baab0e1b05a3a9e068948667412afa7d692e1da3869ca54be4b870

Record source clause organon.grounds.implementations.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1293organon.relationships.roles#p3 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source clause organon.relationships.roles#p3 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1294-/

Close the preceding source-mapping comment without adding a logical condition.

L1295theorem choiceCases012 :

Bundle grounded conventional choices, internal-method reasons and status-only rejection, including the current philosophy.

L1296    (identityImpl.conventional = true ∧ identityImpl.established = true ∧

Keep both actual status facts true for identity.

L1297    JustifiedChoice identityRequirements identityImpl [.status .convention, .method .output]) ∧

Claim justified selection using a list containing convention and an actual output reason; the output reason supplies relevance.

L1298    (Relevant identityRequirements identityImpl (.method .explanation) ∧

Require a faithful explanation reason for the same actual identity implementation.

L1299    Relevant identityRequirements identityImpl (.method .applicability) ∧

Require its actual applicability to cover the required inputs.

L1300    Relevant identityRequirements identityImpl (.method .simplicity) ∧

Require its actual cost to meet the valued simplicity/budget condition.

L1301    Relevant identityRequirements identityImpl (.method .procedure) ∧

Require its actual trace content to meet the valued procedure condition.

L1302    (Relevant identityRequirements cheapSuccessor (.method .simplicity) ∧

Require that cheapSuccessor’s cost reason is actually relevant under the chosen requirements.

L1303      ¬ JustifiedChoice identityRequirements cheapSuccessor [.method .simplicity])) ∧

Nevertheless reject its justified choice with that reason alone because feasibility includes correct outputs.

L1304    (Articulated priorityArticulation ∧ AssessmentAccurate false ∧

Require procedural articulation and a correctly negative report for the same status-priority assessment.

L1305    (∀ selected, Models statusFacts selected) ∧

Keep all candidate interpretations as models of the same actual status facts.

L1306    priorityClaim .identity ∧ ¬ priorityClaim .successor ∧

The priority predicate holds at identity and fails at successor.

L1307    ¬ Entails statusFacts priorityClaim ∧

True name/convention/standing facts do not entail the particular priority claim.

L1308    ¬ JustifiedChoice identityRequirements identityImpl [.status .standing]) ∧

Also reject selecting identity with standing as the only actual reason.

L1309    ((∀ n, identityImpl.run n = wrongExplanation012.run n) ∧

Both implementations return identical actual outputs at every input.

L1310    Feasible identityRequirements identityImpl ∧ Feasible identityRequirements wrongExplanation012 ∧

Both meet the same output and budget feasibility requirements.

L1311    Relevant identityRequirements identityImpl (.method .explanation) ∧

Require a faithful explanation reason for the same actual identity implementation.

L1312    ¬ Relevant identityRequirements wrongExplanation012 (.method .explanation)) ∧

The altered explanation fails that same relevance/content test.

L1313    (¬ choiceSpecification CoreReader.Integration.proposalRequirements

Begin the status-only rejection under the actual proposal-review requirements.

L1314      (CoreReader.Integration.currentPhilosophy CoreReader.Integration.actualSystem CoreReader.Integration.actual).implementation

Use exactly the same current philosophy implementation in this status-only negative branch.

L1315      [.status .standing] ∧

The rejected reason list contains standing alone.

L1316    choiceSpecification CoreReader.Integration.proposalRequirements

State the contrasting justified choice under the same proposal-review requirements.

L1317      (CoreReader.Integration.currentPhilosophy CoreReader.Integration.actualSystem CoreReader.Integration.actual).implementation

Use exactly the same current philosophy implementation in the positive case.

L1318      [.method .output]) ∧

Its actual output performance supplies the positive reason.

L1319    (∀ kind : StatusKind,

Quantify status-only insufficiency over names, conventional use and standing.

L1320    ¬ choiceSpecification identityRequirements identityImpl [.status kind]) :=

Neither name, convention nor standing alone justifies the identity implementation.

L1321  ⟨conventionWithReason, internalReasons, statusAssessmentNonEntailment, internalReasonDistinguishes012, ownPhilosophyStatus012, allStatusOnly012⟩

Combine six choice proofs, retaining real content comparisons and rejecting privilege for the current philosophy.

L1323/- The bundle preserves the full checked propositions of its named component cases. -/

Explain that this bundle repeats full component propositions; named proofs below establish their conjunction.

L1324/-- organon-map CoreReader.Adopted.choiceLimits012

Begin source-tracing metadata for CoreReader.Adopted.choiceLimits012; this mapping is not a proof premise.

L1325organon.grounds.implementations#p1 sha256 bb2a822a304d4a20f513218f356ddbeeca8ee139e3ed802213591e9ff6c5095c

Record source clause organon.grounds.implementations#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1326organon.grounds.implementations#p2 sha256 bb2a822a304d4a20f513218f356ddbeeca8ee139e3ed802213591e9ff6c5095c

Record source clause organon.grounds.implementations#p2 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1327organon.grounds.implementations.limits#p1 sha256 db9b5f1803baab0e1b05a3a9e068948667412afa7d692e1da3869ca54be4b870

Record source clause organon.grounds.implementations.limits#p1 and its displayed SHA-256 identity; this is documentary linkage, not semantic validation.

L1328-/

Close the preceding source-mapping comment without adding a logical condition.

L1329theorem choiceLimits012 :

Bundle limits of openness: one feasible conventional option, unequal internal reasons, broader differences and limited assessment-policy independence.

L1330    ((∀ candidate, Feasible identityRequirements (implementation candidate) ↔ candidate = .identity) ∧

Over the explicitly two-valued candidate type, require feasibility exactly for identity.

L1331    JustifiedChoice identityRequirements identityImpl objectiveReason) ∧

Also retain identity’s actual output-reason justification.

L1332    (identityImpl.conventional = true ∧ identityImpl.established = true ∧

Keep both actual status facts true for identity.

L1333    JustifiedChoice identityRequirements identityImpl [.status .convention, .method .output]) ∧

Claim justified selection using a list containing convention and an actual output reason; the output reason supplies relevance.

L1334    ((∀ n, identityImpl.run n = wrongExplanation012.run n) ∧

Both implementations return identical actual outputs at every input.

L1335    Feasible identityRequirements identityImpl ∧ Feasible identityRequirements wrongExplanation012 ∧

Both meet the same output and budget feasibility requirements.

L1336    Relevant identityRequirements identityImpl (.method .explanation) ∧

Require a faithful explanation reason for the same actual identity implementation.

L1337    ¬ Relevant identityRequirements wrongExplanation012 (.method .explanation)) ∧

The altered explanation fails that same relevance/content test.

L1338    (JustifiedChoice identityRequirements identityImpl objectiveReason ∧

Also retain identity’s actual output-reason justification.

L1339    identityImpl.run 0 ≠ successorImpl.run 0) ∧

Also require that identity and successor actually produce different outputs at input 0.

L1340    ((∀ x, x = 0 → identityImpl.run x = changedOutsideZero.run x) ∧

Compare actual outputs only under the input-0 scope.

L1341    identityImpl.run 1 ≠ changedOutsideZero.run 1) ∧

Separately require a real output difference at input 1.

L1342    ((Articulated priorityArticulation ∧ AssessmentAccurate false ∧

Require procedural articulation and a correctly negative report for the same status-priority assessment.

L1343      (∀ selected, Models statusFacts selected) ∧

Keep all candidate interpretations as models of the same actual status facts.

L1344      priorityClaim .identity ∧ ¬ priorityClaim .successor ∧

The priority predicate holds at identity and fails at successor.

L1345      ¬ Entails statusFacts priorityClaim ∧

The status premises alone still do not entail the priority claim.

L1346      ¬ JustifiedChoice identityRequirements identityImpl [.status .standing]) ∧

Also reject selecting identity with standing as the only actual reason.

L1347    PolicyIndependenceExample) :=

The two policies share the same accurate assessment but differ in their actual priority reasons; this is not full Grounds independence.

L1348  ⟨singleFeasible, conventionWithReason, internalReasonDistinguishes012, openNotEquivalent, localNotGlobal, generalGroundsNotChoice⟩

Use six checked components; generalGroundsNotChoice proves only the disclosed general-assessment/choice-policy separation.

L1350end CoreReader.Adopted

Close CoreReader.Adopted; subsequent declarations are outside this namespace.