leanified/CoreReader/Engineering/Integration.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.

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LeanLine explanation

L1import CoreReader.Engineering.Domain

Import CoreReader.Engineering.Domain, making its declarations and transitive dependencies available; this line adds no new proposition.

L2import CoreReader.Engineering.Reflection

Import CoreReader.Engineering.Reflection, making its declarations and transitive dependencies available; this line adds no new proposition.

L3import CoreReader.Engineering.SelfApplication

Import CoreReader.Engineering.SelfApplication, making its declarations and transitive dependencies available; this line adds no new proposition.

L5namespace CoreReader.Engineering

Open namespace CoreReader.Engineering for the following declarations.

L7open CoreReader.Logic CoreReader.Evidence CoreReader.Adopted

Allow unqualified references to declarations in CoreReader.Logic CoreReader.Evidence CoreReader.Adopted; their meaning is unchanged.

L9/- All interpretations below share this activity, requirements, evidence and

Comment fixes the activity, requirements and evidence shared by all interpretations here.

L10cost limits. Only the selected implementation and its stated value priority vary. -/

Comment also fixes cost limits while permitting the chosen implementation and stated value to vary.

L11abbrev sharedContext : Context := currentContinuing

All integrated claims use sharedContext, definitionally the fixed currentContinuing context.

L13def maintainedOutput (chosen : Candidate) (n : Nat) : Nat :=

For a chosen design and natural input, maintainedOutput extracts one observable result.

L14  (behavior chosen [n]).headD 0

Run behavior on the singleton [n] and take its head, defaulting to 0 if empty.

L16def chosenImplementation (chosen : Candidate) : CoreReader.Choice.Implementation where

Project the chosen design into Core's Implementation record.

L17  name := "order-preserving queue"

Use the shared descriptive name order-preserving queue.

L18  conventional := chosen == .presentSimple

Mark conventional exactly when chosen is presentSimple.

L19  established := chosen == .presentSimple

Mark established under the same Boolean equality.

L20  run := maintainedOutput chosen

Use maintainedOutput as the implementation's actual run function.

L21  cost := abstractionComplexity chosen

Its Core-level cost is the chosen design's abstraction complexity.

L22  domain _ := True

The projected domain permits every natural input.

L23  explanation := maintainedOutput chosen

Use the identical maintainedOutput function as its explanation.

L24  trace n := [maintainedOutput chosen n]

The trace is a singleton containing the final output; it is not an internal execution trace.

L26/- This Core choice projection checks the queue's one-item observable contract

Comment limits the Core choice projection to the queue's one-item observable contract.

L27and present understanding budget. Domain retains its additional required checks. -/

Comment adds present understanding budget and retains separate domain checks outside this projection.

L28def chosenRequirements : CoreReader.Choice.Requirements where

Define the Core choice requirements for this projection.

L29  inputs _ := True

Every natural number is an admissible input.

L30  expected n := n

The expected result is the input itself.

L31  budget := sharedContext.limits.capacity .understanding

Use the shared context's understanding capacity as budget.

L32  values _ := True

The additional values predicate is unrestricted True.

L34def chosenReasons : List CoreReader.Choice.Reason :=

The available Core choice reasons form a finite list.

L35  [.method .output, .method .simplicity]

List output and simplicity method reasons; membership alone will not prove a reason adequate.

L37theorem maintainedOutputCorrect (chosen : Candidate) (n : Nat) :

For every design and natural n, state correctness of the one-item output projection.

L38    maintainedOutput chosen n = n := by

The actual maintainedOutput must equal n.

L39  rfl

The equality is definitional for singleton input, so reflexivity proves it.

L41theorem implementationReasoned (chosen : Candidate)

Prove reasoned Core implementation choice for any chosen design under a budget premise.

L42    (budget : abstractionComplexity chosen ≤ chosenRequirements.budget) :

Assume actual abstraction complexity is within chosenRequirements.budget.

L43    choiceSpecification chosenRequirements (chosenImplementation chosen) chosenReasons := by

The conclusion uses the actual requirements, projected implementation and listed reasons.

L44  refine ⟨⟨fun n _ => maintainedOutputCorrect chosen n, budget⟩,

Construct functional correctness for every allowed input and reuse the supplied budget proof.

L45    .method .output, ?_, ?_⟩

Choose the output method reason; leave its membership and adequacy obligations.

L46  · simp [chosenReasons]

Unfold chosenReasons to establish membership of the output reason.

L47  · exact ⟨trivial, fun n _ => maintainedOutputCorrect chosen n⟩

Prove the output reason's unrestricted value condition and exact input/output contract.

L49/- This reported capability concerns actual paths for each maintainer. Zero

Comment identifies the capability report as actual maintainer-indexed path availability.

L50records the unavailable path, not an assertion that an unsupported path exists. -/

Comment explains 0 as a missing-path marker, not evidence that a path exists.

L51def capabilityOutput (chosen : Candidate) (input : Nat) : Nat :=

capabilityOutput reports revision-path work for a maintainer encoded by a natural input.

L52  let maintainer := if input = 0 then Maintainer.original

Input 0 selects the original maintainer.

L53    else if input = 1 then Maintainer.successor else Maintainer.agent

Input 1 selects the successor; every larger input selects the agent.

L54  if decide (CanChange sharedContext.activity chosen maintainer .designRevision)

Decide actual CanChange for this maintainer, design and designRevision in sharedContext.

L55  then changeWork chosen .designRevision else 0

Return actual revision work when the path exists, otherwise 0 as an absence marker.

L57def engineeringProcess (chosen : Candidate) : Process :=

Build a Process reporting the chosen design's capability-output function.

L58  ⟨capabilityOutput chosen, none⟩

Its output is capabilityOutput; its optional explanation is none.

L60def engineeringCapability (chosen : Candidate) : Claim Process :=

Define the exact functional claim on a Process for this chosen design.

L61  fun process => ∀ input, process.output input = capabilityOutput chosen input

For all natural inputs, require the process output to equal capabilityOutput for that design.

L63theorem engineeringCapabilityGrounded (chosen : Candidate) :

Ground the functional capability claim for every chosen design.

L64    capabilitySpecification (engineeringProcess chosen) (engineeringCapability chosen) := by

The process and capability specification share the same chosen parameter.

L65  exact grounds012Singleton _ (processContractDischarged _ _ (fun _ => rfl))

Use an inferential process-contract facet discharged by pointwise reflexivity, then singleton grounds.

L67theorem actualCapabilityContrast :

actualCapabilityContrast computes six concrete maintainer/design outputs.

L68    (engineeringProcess .presentSimple).output 0 = 17 ∧

presentSimple reports 17 work units for the original maintainer.

L69    (engineeringProcess .presentSimple).output 1 = 0 ∧

It reports absent-path marker 0 for the successor.

L70    (engineeringProcess .presentSimple).output 2 = 0 ∧

It also reports 0 for the agent.

L71    (engineeringProcess .evolvable).output 0 = 6 ∧

evolvable reports 6 work units for the original maintainer.

L72    (engineeringProcess .evolvable).output 1 = 6 ∧

It reports 6 for the successor too.

L73    (engineeringProcess .evolvable).output 2 = 6 := by decide

It reports 6 for the agent; decide computes all six equalities.

L75/- A recorded threshold test measures present abstraction complexity in this

Comment introduces a recorded threshold of present abstraction complexity.

L76finite model. It does not observe future maintainability or establish a value. -/

Comment confines that observation to this finite model and excludes future maintainability and value establishment.

L77def presentBudgetRecord : Record Candidate :=

Create one recorded Boolean threshold observation over Candidate.

L78  ⟨fun candidate => decide (abstractionComplexity candidate ≤ 3), true⟩

The instrument checks abstraction complexity ≤ 3, and the recorded result is true.

L80abbrev presentBudgetClaim : Claim Candidate := fun candidate => abstractionComplexity candidate ≤ 3

presentBudgetClaim is precisely the same complexity-at-most-3 predicate.

L82theorem budgetObservationMeaning (candidate : Candidate) :

For every candidate, relate compatibility with this record to its exact claim.

L83    Compatible [presentBudgetRecord] candidate ↔ presentBudgetClaim candidate := by

State an iff; the record constrains only present complexity.

L84  constructor

Prove each direction of the equivalence separately.

L85  · intro observed

Assume compatibility with the singleton observation list.

L86    have result := observed presentBudgetRecord (List.mem_singleton.mpr rfl)

Apply compatibility to its actual record using singleton membership.

L87    exact of_decide_eq_true result

Convert the instrument's true Boolean result to the complexity proposition.

L88  · intro enough record member

Conversely, assume the bound and introduce any listed record.

L89    cases List.mem_singleton.mp member

Singleton membership identifies it as presentBudgetRecord.

L90    exact decide_eq_true enough

Convert the bound into the required Boolean equality to true.

L92def budgetEmpiricalFacet : Facet Candidate :=

Package the budget observation into an empirical Facet over Candidate.

L93  .empirical [presentBudgetRecord] (fun _ => True) presentBudgetClaim (fun _ => True)

Use the exact record and budget claim; both empirical scope and uncertainty predicates are True.

L95theorem budgetEmpiricalDischarged : FacetDischarged budgetEmpiricalFacet := by

Prove actual discharge of that empirical facet.

L96  refine ⟨⟨.evolvable, (budgetObservationMeaning _).2 (by decide), trivial⟩, ?_, ?_⟩

Use evolvable as a compatible in-scope witness; leave claim support and uncertainty support to prove.

L97  · intro candidate observed _

For every compatible candidate, introduce the trivial empirical-scope premise.

L98    exact (budgetObservationMeaning candidate).1 observed

Use the forward observation equivalence to prove the exact budget claim.

L99  · intro _ _; trivial

The remaining uncertainty predicate is True, so every compatible candidate satisfies it trivially.

L101def capacityClaim : Claim Candidate :=

capacityClaim is a proposition about the actual current understanding capacity.

L102  fun candidate => abstractionComplexity candidate ≤ sharedContext.limits.capacity .understanding

For each candidate require complexity ≤ sharedContext's understanding limit, which is 12.

L104def capacityAssumptions : Theory Candidate := singleton presentBudgetClaim

The capacity inference assumes only the singleton presentBudgetClaim theory.

L106def budgetInferentialFacet : Facet Candidate := .inferential capacityAssumptions capacityClaim

Construct the inferential facet from those assumptions to the capacity claim.

L108theorem budgetInferentialDischarged : FacetDischarged budgetInferentialFacet := by

Prove this inference has a model and entails its claim.

L109  refine ⟨⟨.evolvable, (modelsSingleton _ _).2 (by decide)⟩, ?_⟩

Use evolvable to witness the complexity-at-most-3 assumptions, leaving entailment.

L110  intro candidate premises

Introduce any candidate satisfying all inference premises.

L111  have small := (modelsSingleton _ _).1 premises

Singleton-model equivalence extracts the ≤ 3 bound.

L112  exact Nat.le_trans small (by decide)

Combine that bound with the computed 3 ≤ 12 inequality.

L114def budgetScopeAccount : ScopeAccount Candidate where

Build a scope account for the present-budget measurement claim.

L115  claim := presentBudgetClaim

The explained claim is exactly presentBudgetClaim.

L116  conditions := fun _ => True

Application conditions are unrestricted True.

L117  observationScope := fun _ => True

Observation scope is likewise True.

L118  relevant := fun a b => behavior a [2, 1, 2] = behavior b [2, 1, 2]

Comparative relevance means equal actual behavior on [2, 1, 2].

L119  compared := fun a b => presentBudgetClaim a ∧ presentBudgetClaim b

Two candidates are compared only when both satisfy the budget claim.

L120  used method := method = .measurement

The only used method is measurement.

L121  role _ := "threshold observation of present complexity; no future-performance conclusion"

The role text limits the observation to current complexity and excludes future-performance conclusions.

L122  explains method text claim conditions := method = .measurement ∧

The explanation relation first requires the method to be measurement.

L123    text = "threshold observation of present complexity; no future-performance conclusion" ∧

Require the exact stored limitation text.

L124    claim = presentBudgetClaim ∧ conditions = (fun _ => True)

Require identity of the explained claim and condition predicate.

L126theorem budgetScopeExplained : scopeSpecification budgetScopeAccount := by

Verify the stated scopeSpecification of this exact account.

L127  constructor

Split comparative-scope and method-explanation obligations.

L128  · intro a b _; exact ⟨trivial, trivial, trivial, trivial, rfl⟩

For compared candidates, prove four True conditions/scopes and use definitional equality of their actual behavior on [2,1,2] for relevance.

L129  · intro method hm

Introduce any actually used method and its usage proof.

L130    exact ⟨by change "threshold observation of present complexity; no future-performance conclusion" ≠ ""; decide,

Prove the role string is nonempty by computing its inequality with the empty string.

L131      hm, rfl, rfl, rfl⟩

Reuse usage equality and reflexive identities for text, claim and conditions.

L133/- The unchanged observation cannot justify a stronger complexity bound. -/

Comment introduces a counterexample to strengthening a claim without changing its observation.

L134theorem budgetObservationLimit :

Demonstrate that this observation does not support a stricter complexity bound.

L135    Compatible [presentBudgetRecord] .evolvable ∧

evolvable is compatible with the recorded ≤ 3 result.

L136    ¬ Supports [presentBudgetRecord] (fun candidate => abstractionComplexity candidate ≤ 1) := by

Yet the singleton record does not support the universal compatible-world claim complexity ≤ 1.

L137  refine ⟨(budgetObservationMeaning _).2 (by decide), ?_⟩

Prove compatibility via the observation equivalence, leaving failure of support.

L138  intro support

Assume the stronger support relation for contradiction.

L139  have impossible := support .evolvable ((budgetObservationMeaning _).2 (by decide))

Apply it to compatible evolvable, obtaining the impossible 3 ≤ 1.

L140  exact (by decide : ¬ (3 ≤ 1)) impossible

Compute ¬(3 ≤ 1) and apply it to that derived bound.

L142/- The policy values expansion while keeping every represented organization,

Comment states that the policy values expansion while retaining revisability of represented forms.

L143method and principle form revisable. It does not assert that a revision occurs. -/

Comment includes organizations, methods and principles, but does not assert an actual revision event.

L144def engineeringPolicy : CoreReader.Agency.Policy where

Instantiate an Agency.Policy for this engineering activity.

L145  worthPursuing aim :=

Define which aims count as worth pursuing.

L146    (aim = .expandUnderstandingAndConstruction ∧ coreAdopted .generation = true) ∨

Expansion is worthwhile when the generation commitment is explicitly adopted.

L147      aim = .preserveSafeOperation

Preserving safe operation is also worthwhile unconditionally.

L148  current form := form.version = 1

A form is current exactly when its version equals 1.

L149  revisable form := ∃ next, form.version < next ∧ coreAdopted .generation = true

Revisability requires some greater natural-number version and generation adoption.

L150  permitsVersion old next := old ≤ next

Permit any nondecreasing version transition.

L152theorem engineeringGenerative : generationSpecification engineeringPolicy := by

Prove the generation specification for this concrete policy.

L153  exact ⟨Or.inl ⟨rfl, rfl⟩, fun form _ => ⟨form.version + 1, Nat.lt_succ_self _, rfl⟩⟩

Witness adopted expansion and, for every current form, choose version + 1 as a strictly greater revisable version.

L155/- Own facts are mathematical reports about this model and its recorded state.

Comment identifies OwnFact values as mathematical reports of this model's state.

L156Their inferential tasks do not replace the separate empirical or value tasks. -/

Comment preserves the separate empirical/value tasks despite these reports' inferential grounds.

L157inductive OwnFact

OwnFact enumerates model reports that will be held in its theory.

L158  | selected | requirements | capacity | capability | forecast | revision

Include selection, requirements, capacity, capability, forecast and revision reports.

L159  | generativePolicy | reflection | coreAdoption (principle : CoreCommitment)

Also include generation/reflection reports and an adoption report parameterized by principle.

L160  deriving DecidableEq, Repr

Derive DecidableEq, Repr: decidable equality and printable representations of these constructors.

L162abbrev ownFactClaim (adopted : Candidate) : OwnFact → Claim Candidate

Interpret each OwnFact as a claim on Candidate, parameterized by the adopted design.

L163  | .selected => fun candidate => candidate = adopted

The selection report requires the candidate to equal the adopted design.

L164  | .requirements => fun candidate => Meets sharedContext.required (sharedContext.profiles candidate)

The requirements report uses that candidate's actual profile in sharedContext.

L165  | .capacity => capacityClaim

The capacity report is the previously defined actual capacity claim.

L166  | .capability => fun candidate => engineeringCapability candidate (engineeringProcess candidate)

The capability report applies the candidate-indexed claim to the same candidate's process.

L167  | .forecast => fun _ => staticBatch 21 10 = liveBatch 21 10 ∧ staticBatch 21 5 ≠ liveBatch 21 5

The forecast report states old size-10 agreement and size-5 disagreement, independent of candidate.

L168  | .revision => fun candidate => RevisionAccount (revisionFor sharedContext candidate)

The revision report concerns the actual revisionFor sharedContext candidate account.

L169  | .generativePolicy => fun _ => generationSpecification engineeringPolicy

The policy report states generationSpecification of the actual engineeringPolicy.

L170  | .reflection => fun candidate => reflexivitySpecification

The reflection report uses the candidate's actual reflexivity specification.

L171      (selfModel candidate).rules (selfModel candidate).self (selfModel candidate).performed

Rules, self targets and performed records all come from that same selfModel candidate.

L172  | .coreAdoption principle => (governancePosition principle).commitment

The adoption report is the same principle's governance commitment predicate.

L174theorem actualOwnFact (chosen : Candidate)

Prove each own fact about the actually selected design.

L175    (ordinary : chosen = .presentSimple ∨ chosen = .evolvable) (fact : OwnFact) :

Require an ordinary design, but quantify universally over OwnFact.

L176    ownFactClaim chosen fact chosen := by

Evaluate the adopted-indexed fact at that same chosen candidate.

L177  cases fact with

Split on the fact constructor.

L178  | selected => rfl

The selection report is chosen = chosen, proved reflexively.

L179  | requirements => cases chosen <;> decide

For requirements, enumerate all three candidates and compute their necessary-profile checks.

L180  | capacity => rcases ordinary with rfl | rfl <;> change _ ≤ 12 <;> decide

For capacity, restrict to the two ordinary candidates and compute complexity ≤ 12.

L181  | capability => intro _; rfl

For capability, introduce any input and use the identical output function reflexively.

L182  | forecast => exact ⟨rfl, by decide⟩

For forecast, combine definitional old equality with computed new inequality.

L183  | revision => rcases ordinary with rfl | rfl <;> decide

For revision, substitute each ordinary design and decide its concrete account.

L184  | generativePolicy => exact engineeringGenerative

Reuse engineeringGenerative for the policy report.

L185  | reflection => exact currentSelfApplication chosen ordinary

Reuse actual currentSelfApplication under the ordinary premise.

L186  | coreAdoption _ => rfl

The Core adoption flag is true by definitional equality.

L188def ownFactPremises (chosen : Candidate) : Theory Candidate :=

Define the exact inference assumptions for facts about the chosen design.

L189  singleton (fun candidate => candidate = chosen)

The sole assumption is that the candidate equals chosen; this is an identity-conditioned inference.

L191theorem actualOwnFactGrounded (chosen : Candidate)

Ground every own-fact report inferentially.

L192    (ordinary : chosen = .presentSimple ∨ chosen = .evolvable) (fact : OwnFact) :

Keep the ordinary-design premise and universally selected fact.

L193    inferentialSpecification (ownFactPremises chosen) (ownFactClaim chosen fact) := by

Use the identity theory as premises and the actual fact interpretation as conclusion.

L194  apply grounds012Singleton

Reduce singleton grounds to discharge of its inferential facet.

L195  refine ⟨⟨chosen, (modelsSingleton _ _).2 rfl⟩, ?_⟩

Supply chosen as a model of its own identity premise; leave entailment.

L196  intro candidate same

Introduce an arbitrary candidate satisfying that identity theory.

L197  have identity := (modelsSingleton _ _).1 same

Extract candidate = chosen using singleton-model equivalence.

L198  subst candidate

Replace candidate by chosen throughout the goal.

L199  exact actualOwnFact chosen ordinary fact

Apply the actually proved own-fact theorem for the same chosen design and fact.

L201/- In this fixed applicable context, the actual priority rule and the adopted

Comment restricts the priority/value equivalence to this fixed applicable context.

L202evolution value select exactly the same candidate. This identity connects its

Comment states that both predicates select exactly the same candidate.

L203value grounds to the normative rule, not merely to an adoption label. -/

Comment connects value grounds to actual normative content through identity, rather than a mere adoption label.

L204theorem priorityValueMeaning (candidate : Candidate) :

For every candidate in the fixed shared context, prove value commitment and actual priority select identically.

L205    (selectionPosition .evolvable).commitment candidate ↔

The left side is the commitment of the explicitly adopted evolvable selection position.

L206      EvolutionPriority sharedContext candidate := by

The right side is EvolutionPriority itself, not a label naming priority.

L207  constructor

Prove both directions of this same-claim equivalence.

L208  · intro selected

Assume the evolvable selection commitment.

L209    change candidate = .evolvable at selected

Expose that commitment as candidate = evolvable.

L210    subst candidate

Substitute the actually selected evolvable candidate.

L211    exact currentDomainSatisfied.2.1

Extract its priority proof from actual currentDomainSatisfied.

L212  · intro priority

Conversely assume actual EvolutionPriority for the candidate.

L213    exact (priorityWhenApplicable sharedContext candidate priority

Apply the priority rule's selected-candidate conclusion in sharedContext.

L214      currentPriorityConditions currentNoThreat.2).1

Supply current applicability and absence of justified departure; these fixed-context facts are essential.

L216theorem priorityGrounds :

priorityGrounds supplies value grounds for the actual priority proposition in sharedContext.

L217    Grounds012 (EvolutionPriority sharedContext) canonicalArticulation

The claim is EvolutionPriority sharedContext, with canonical articulation.

L218      [.value (selectionPosition .evolvable)] (.value (selectionPosition .evolvable)) := by

Use the exact evolvable value facet both as the singleton required task and the supplied facet.

L219  have same : (selectionPosition .evolvable).commitment = EvolutionPriority sharedContext :=

Introduce equality between the value commitment predicate and actual priority predicate.

L220    funext (fun candidate => propext (priorityValueMeaning candidate))

Use propositional extensionality pointwise and function extensionality to derive that predicate equality.

L221  rw [← same]

Rewrite the priority claim back to the identical value commitment claim.

L222  exact selectionGrounded .evolvable (Or.inr rfl)

Reuse selectionGrounded for evolvable; no facet or assessed claim is swapped without this equality.

L224/- Facts of adoption remain distinct from the actual normative contents. Each

Comment separates adoption facts from actual normative contents.

L225constructor below denotes its full represented duty, with its original task,

Comment states that each following constructor retains the full represented duty and original task.

L226conditions, reasons and scope. Domain duties enter only for the domain adopter.

Comment retains conditions/reasons/scope and restricts domain duties to the domain adopter.

L227Consistency is the constraint on the resulting whole theory below; it is not

Comment places consistency as an external constraint on the complete resulting theory.

L228encoded as a self-referential proposition in that theory's own definition. -/

Comment avoids defining that theory through a self-referential proposition asserting its own consistency.

L229inductive OwnNorm

OwnNorm enumerates full represented duties separately from adoption reports.

L230  | generation | reflection | empirical | inferential | principleValue (principle : CoreCommitment)

Include generation, reflection, empirical/inferential grounds and principle-indexed value grounds.

L231  | selectionValue | scope | capability | choice | ownGrounds (fact : OwnFact)

Include selection value, scope, capability, choice and fact-indexed inferential grounds.

L232  | domain | priorityValue

Include the domain bundle and grounds for actual priority as distinct duties.

L233  deriving DecidableEq, Repr

Derive DecidableEq, Repr: decidable equality and printable representations of these constructors.

L235def normApplies (adopted : Candidate) : OwnNorm → Prop

normApplies determines adoption-dependent membership eligibility for each norm.

L236  | .domain | .priorityValue => adopted = .evolvable

Only the evolvable adopter includes domain and priority-value duties under this predicate.

L237  | _ => True

Every other norm applies to all adopters.

L239def ownNormClaim (adopted : Candidate) : OwnNorm → Claim Candidate

Interpret every OwnNorm as its full proposition on Candidate, retaining the adopted parameter.

L240  | .generation => fun _ => generationSpecification engineeringPolicy

The generation norm is the actual policy's full generationSpecification.

L241  | .reflection => fun candidate => reflexivitySpecification

The reflection norm requires the candidate's actual reflexivity specification.

L242      (selfModel candidate).rules (selfModel candidate).self (selfModel candidate).performed

It uses that same candidate model's rules, self relation and performance relation.

L243  | .empirical => fun _ => empiricalSpecification [presentBudgetRecord] (fun _ => True)

The empirical norm retains the actual record and original True empirical-scope predicate.

L244      presentBudgetClaim (fun _ => True)

It also retains the exact budget claim and the original True uncertainty predicate.

L245  | .inferential => fun _ => inferentialSpecification capacityAssumptions capacityClaim

The inferential norm retains actual capacity assumptions and capacity conclusion.

L246  | .principleValue principle => fun _ => valueSpecification (governancePosition principle)

Each principle-value norm requires the full grounds of that same governance position.

L247  | .selectionValue => fun candidate => valueSpecification (selectionPosition adopted) ∧

Selection-value content requires its full value specification, indexed by adopted.

L248      (selectionPosition adopted).commitment candidate

It additionally requires that same value commitment to hold at the candidate.

L249  | .scope => fun _ => scopeSpecification budgetScopeAccount

The scope norm is the exact budgetScopeAccount specification.

L250  | .capability => fun candidate => capabilitySpecification

The capability norm retains the complete capability specification.

L251      (engineeringProcess candidate) (engineeringCapability candidate)

The process and claim both use the same candidate parameter.

L252  | .choice => fun candidate => choiceSpecification

The choice norm retains complete reasoned implementation choice.

L253      chosenRequirements (chosenImplementation candidate) chosenReasons

It uses actual requirements, this candidate's implementation and the original reasons.

L254  | .ownGrounds fact => fun _ => inferentialSpecification

Each own-ground norm is the full inferential task for its fact.

L255      (ownFactPremises adopted) (ownFactClaim adopted fact)

Its identity premises and actual fact claim are both indexed by adopted.

L256  | .domain => fun candidate => DomainSatisfied sharedContext candidate

The domain norm is actual DomainSatisfied in sharedContext, evaluated at candidate.

L257  | .priorityValue => fun _ => Grounds012 (EvolutionPriority sharedContext) canonicalArticulation

The priority-value norm is grounds for the actual priority predicate, with canonical articulation.

L258      [.value (selectionPosition .evolvable)] (.value (selectionPosition .evolvable))

Retain the same required and supplied evolvable value facet.

L260theorem actualOwnNorm (chosen : Candidate)

actualOwnNorm proves satisfaction of each applicable full norm at the selected candidate.

L261    (ordinary : chosen = .presentSimple ∨ chosen = .evolvable)

The selected candidate must again be one of the two ordinary designs.

L262    (norm : OwnNorm) (applicable : normApplies chosen norm) : ownNormClaim chosen norm chosen := by

Quantify over the norm and assume its actual normApplies condition before concluding its content.

L263  cases norm with

Split on every OwnNorm constructor, retaining its parameters.

L264  | generation => exact engineeringGenerative

Discharge generation with the actual engineering-policy theorem.

L265  | reflection => exact currentSelfApplication chosen ordinary

Discharge reflection with the checked self-model theorem for this ordinary design.

L266  | empirical => exact grounds012Singleton _ budgetEmpiricalDischarged

Use the actually discharged empirical facet inside singleton grounds.

L267  | inferential => exact grounds012Singleton _ budgetInferentialDischarged

Use the actually discharged capacity inference facet likewise.

L268  | principleValue principle => exact governanceGrounded principle

Use governanceGrounded for this exact principle parameter.

L269  | selectionValue => exact ⟨selectionGrounded chosen ordinary, rfl⟩

Pair actual selection grounds with reflexive selected/adopted identity.

L270  | scope => exact budgetScopeExplained

Reuse the actual budget scope explanation proof.

L271  | capability => exact engineeringCapabilityGrounded chosen

Reuse the same candidate's actual functional capability grounds.

L272  | choice =>

Enter the reasoned implementation choice obligation.

L273    apply implementationReasoned

Apply implementationReasoned, leaving its actual budget premise.

L274    rcases ordinary with rfl | rfl <;> change _ ≤ 12 <;> decide

Substitute either ordinary design and compute its complexity ≤ 12.

L275  | ownGrounds fact => exact actualOwnFactGrounded chosen ordinary fact

Use actualOwnFactGrounded for the very same chosen design and indexed fact.

L276  | domain =>

For the domain norm, use its adoption applicability premise.

L277    change chosen = .evolvable at applicable

Expose applicable as chosen = evolvable.

L278    subst chosen

Substitute evolvable for chosen.

L279    exact currentDomainSatisfied

Now use the actual full current domain satisfaction proof.

L280  | priorityValue => exact priorityGrounds

The fixed priority-value norm is discharged by priorityGrounds.

L282def ownFactTheory (chosen : Candidate) : Theory Candidate :=

ownFactTheory holds exactly the represented own-fact claims.

L283  fun claim => ∃ fact : OwnFact, claim = ownFactClaim chosen fact

A claim is held if some OwnFact interprets to that exact claim.

L285def ownNormTheory (chosen : Candidate) : Theory Candidate :=

ownNormTheory holds applicable full normative contents.

L286  fun claim => ∃ norm : OwnNorm, normApplies chosen norm ∧ claim = ownNormClaim chosen norm

Require an actual norm witness, its normApplies proof and equality with its full interpreted claim.

L288/- The consequence relation now acts on all these facts and normative contents

Comment says the consequence relation applies jointly to facts and full normative contents.

L289together, including the implications of their union. -/

Comment includes implications of their actual union, not just separate checks of each branch.

L290def ownTheory (chosen : Candidate) : Theory Candidate :=

ownTheory is the combined theory on which later model and consistency predicates operate.

L291  union (ownFactTheory chosen) (ownNormTheory chosen)

Take the union of factual reports and full applicable normative claims; it is not merely an adoption-marker theory.

L293theorem allNormativeContentHeld (chosen : Candidate) (norm : OwnNorm)

For every chosen design and norm, provide a route into the combined theory.

L294    (applicable : normApplies chosen norm) : ownTheory chosen (ownNormClaim chosen norm) :=

An actual applicability premise suffices to hold that norm's exact full claim.

L295  Or.inr ⟨norm, applicable, rfl⟩

Use the union's normative branch with norm witness, applicability and reflexive claim identity.

L297theorem nonemptyOwnObjects (chosen : Candidate) :

Exhibit nonempty held claims and review objects for every chosen design.

L298    ownTheory chosen (ownFactClaim chosen .selected) ∧

The chosen selection report is actually in ownTheory.

L299    ownTheory chosen (ownFactClaim chosen (.coreAdoption .grounds)) ∧

The grounds-principle adoption report is also actually held.

L300    (.activity : ReviewObject) ∈ (selfModel chosen).objects ∧

The activity review object belongs to selfModel's list.

L301    (.commitment .grounds : ReviewObject) ∈ (selfModel chosen).objects := by

The grounds commitment object belongs to that same list.

L302  refine ⟨Or.inl ⟨.selected, rfl⟩, Or.inl ⟨.coreAdoption .grounds, rfl⟩, ?_, ?_⟩ <;>

Supply two factual-branch witnesses and leave the two object membership checks.

L303    simp [selfModel, reviewObjects, coreCommitments]

Expand actual model and finite commitment lists to prove those memberships.

L305def comparisonContext (chosen : Candidate) : CoreReader.Logic.Context Candidate OwnFact where

comparisonContext is a Logic.Context with worlds Candidate and questions OwnFact.

L306  assumptions := ownFactPremises chosen

Its assumptions are the exact chosen-identity theory.

L307  meaning := ownFactClaim chosen

Its question meaning is the chosen-indexed factual interpretation.

L308  scope := valueScope

Its admissible comparison scope requires complexity at most 3.

L310def engineeringSnapshot (chosen : Candidate) (revision : Nat) : Snapshot Candidate OwnFact :=

Build a Snapshot from a chosen design and explicit revision number.

L311  ⟨ownTheory chosen, comparisonContext chosen, revision⟩

Store the full combined theory, its comparison context and that revision number.

L313theorem currentAdmissible (chosen : Candidate)

Prove the chosen ordinary design is an actual admissible world of its combined theory.

L314    (ordinary : chosen = .presentSimple ∨ chosen = .evolvable) :

Keep the ordinary-design premise explicit.

L315    Admissible (ownTheory chosen) (comparisonContext chosen) chosen := by

Admissibility includes all held claims, comparison assumptions and scope at the same chosen world.

L316  refine ⟨?_, (modelsSingleton _ _).2 rfl, ?_⟩

Supply reflexive identity assumptions; leave full theory satisfaction and scope.

L317  · intro claim held

Introduce any claim actually held in the combined theory.

L318    rcases held with factHeld | normHeld

Split union membership into the factual and normative branches.

L319    · obtain ⟨fact, rfl⟩ := factHeld

Extract the OwnFact witness and substitute its exact claim interpretation.

L320      exact actualOwnFact chosen ordinary fact

Apply the checked actualOwnFact theorem at chosen.

L321    · obtain ⟨norm, applicable, rfl⟩ := normHeld

Extract the OwnNorm witness, applicability proof and exact claim identity.

L322      exact actualOwnNorm chosen ordinary norm applicable

Apply actualOwnNorm with the same chosen design, norm and applicability proof.

L323  · rcases ordinary with rfl | rfl <;> change _ ≤ 3 <;> decide

For scope, substitute each ordinary design and compute complexity ≤ 3.

L325theorem currentConsistency (chosen : Candidate)

Prove consistency of the new full snapshot plus truthful change reporting against the specified earlier snapshot; this does not merge old and new theories.

L326    (ordinary : chosen = .presentSimple ∨ chosen = .evolvable) :

The new choice must be ordinary.

L327    consistencySpecification (engineeringSnapshot .evolvable 0)

The earlier snapshot is evolvable at revision 0.

L328      (engineeringSnapshot chosen 1) true := by

The current snapshot is chosen at revision 1, with change acknowledged as true.

L329  exact ⟨consequenceConsistency _ _ ⟨chosen, currentAdmissible chosen ordinary⟩, fun _ => rfl⟩

Use the actual admissible chosen witness to establish consequence consistency, and reflexivity for the change-record obligation.

L331theorem wholeClaimGrounded (chosen : Candidate)

Ground every claim in the combined theory, including full applicable norm claims.

L332    (ordinary : chosen = .presentSimple ∨ chosen = .evolvable)

Require the chosen design to be ordinary.

L333    (claim : Claim Candidate) (held : ownTheory chosen claim) :

Quantify over any Candidate claim and assume it is actually held in ownTheory.

L334    inferentialSpecification (ownFactPremises chosen) claim := by

The conclusion is identity-conditioned inferential grounds for that exact claim.

L335  apply grounds012Singleton

Reduce singleton grounds to the inferential task.

L336  refine ⟨⟨chosen, (modelsSingleton _ _).2 rfl⟩, ?_⟩

Use chosen as the nonempty identity-premise model; leave entailment.

L337  intro candidate same

Introduce any candidate satisfying the identity assumptions.

L338  have identity := (modelsSingleton _ _).1 same

Extract its equality to chosen from singleton-model semantics.

L339  subst candidate

Substitute chosen for that candidate.

L340  exact (currentAdmissible chosen ordinary).1 claim held

Project full theory satisfaction from currentAdmissible and apply it to the exact held claim.

L342/- Keeping the same adoption marker does not conceal contradictory normative

Comment introduces incompatible contents while keeping an adoption marker unchanged.

L343contents. Both demands act on the very same candidate, question and scope. -/

Comment identifies the same candidate, question and scope on both sides of the conflict.

L344def incompatibleNormTheory : Theory Candidate :=

Define a deliberately incompatible normative theory over the same Candidate worlds.

L345  union (singleton (fun candidate => candidate = .presentSimple))

The first singleton theory requires the candidate to be presentSimple.

L346    (singleton (fun candidate => candidate ≠ .presentSimple))

The second requires that same candidate not to be presentSimple.

L348def incompatibleNormContext : CoreReader.Logic.Context Candidate Unit :=

Use one Unit question to compare these opposing claims in a common context.

L349  ⟨emptyTheory, fun _ candidate => candidate = .presentSimple, fun _ => True⟩

Assumptions are empty, the question means candidate = presentSimple, and scope is True.

L351theorem normativeContentVariation :

normativeContentVariation shows a true adoption marker cannot conceal incompatible contents.

L352    coreAdopted .choice = true ∧

The choice adoption flag remains true.

L353    ¬ Consistent incompatibleNormTheory incompatibleNormContext ∧

The actual incompatible theory is nevertheless inconsistent in its shared context.

L354    normApplies .evolvable .domain ∧ ¬ normApplies .presentSimple .domain ∧

Domain adoption applies to evolvable and does not apply to presentSimple.

L355    ownTheory .evolvable (ownNormClaim .evolvable .domain) ∧

The actual domain claim is held in evolvable's theory.

L356    ¬ ownTheory .presentSimple (ownNormClaim .presentSimple .domain) := by

That actual domain claim is not held in presentSimple's theory.

L357  refine ⟨rfl, ?_, rfl, by unfold normApplies; decide, allNormativeContentHeld _ _ rfl, ?_⟩

Construct the adoption and applicability facts and positive membership; leave inconsistency and negative membership.

L358  · apply conflictRequiresChange _ _ ()

Apply conflictRequiresChange to the single shared Unit question.

L359    · intro candidate admissible

For any admissible candidate, derive the positive side of the conflict.

L360      change candidate = .presentSimple

Expose the positive question meaning as candidate = presentSimple.

L361      exact (modelsSingleton (fun c : Candidate => c = .presentSimple) candidate).1

Extract the positive claim via singleton-model equivalence.

L362        ((modelsUnion _ _ _).1 admissible.1).1

Select the first theory from the model of the union inside admissibility.

L363    · intro candidate admissible

For the same kind of admissible candidate, derive the negative side.

L364      change candidate ≠ .presentSimple

Expose the negated meaning as candidate ≠ presentSimple.

L365      exact (modelsSingleton (fun c : Candidate => c ≠ .presentSimple) candidate).1

Extract the negative claim via its singleton-model equivalence.

L366        ((modelsUnion _ _ _).1 admissible.1).2

Select the second theory from the same union model.

L367  · intro held

For negative membership, assume the actual domain claim is held by presentSimple.

L368    have domain := (currentAdmissible .presentSimple (Or.inl rfl)).1 _ held

Its checked admissibility then makes that full DomainSatisfied claim true at presentSimple.

L369    exact currentSimpleViolates domain.2.1

Extract priority from that domain bundle and contradict currentSimpleViolates.

L371/- Every field is an actual satisfaction or support condition. Value accounts

Comment describes Inherited fields as actual satisfaction or support conditions.

L372and assessment completion do not replace the normative fields they explain.

Comment denies that value accounts or completed assessments replace the normative fields themselves.

L373The identity field limits this implementation to its disclosed common context. -/

Comment explicitly limits this implementation to the shared context through its identity field.

L374structure Inherited (ctx : Context) (chosen : Candidate) : Prop where

Inherited bundles represented inherited duties at an explicit context and chosen design; its fields are premises for projection theorems.

L375  sameContext : ctx = sharedContext

Restrict ctx to the exact sharedContext; this is stronger than an arbitrary-context implementation.

L376  generation : generationSpecification engineeringPolicy

Require full generationSpecification for the actual engineering policy.

L377  consistency : consistencySpecification (engineeringSnapshot .evolvable 0)

Require consistency of the current snapshot and truthful reporting against the earlier evolvable revision-0 snapshot.

L378    (engineeringSnapshot chosen 1) true

The current snapshot uses this chosen design at revision 1, with change recorded true.

L379  reflection : reflexivitySpecification (selfModel chosen).rules (selfModel chosen).self

Require reflexivity using this candidate's actual rules and self targets.

L380    (selfModel chosen).performed

The performance relation comes from the same candidate's selfModel.

L381  ownPrincipleGrounds : ∀ principle, valueSpecification (governancePosition principle)

For every Core principle, require the actual governance-position value grounds.

L382  choiceValueGrounds : valueSpecification (selectionPosition chosen)

Require grounds for this chosen design's selection value position.

L383  empiricalGrounds : empiricalSpecification [presentBudgetRecord] (fun _ => True)

Require the empirical task with the actual budget record and True empirical scope.

L384    presentBudgetClaim (fun _ => True)

Retain its exact present-budget claim and True uncertainty predicate; no quantitative uncertainty bound is supplied.

L385  inferentialGrounds : inferentialSpecification capacityAssumptions capacityClaim

Require actual inference from capacityAssumptions to capacityClaim.

L386  scopeAccount : scopeSpecification budgetScopeAccount

Require the actual budget-scope explanation.

L387  capabilityGrounds : capabilitySpecification (engineeringProcess chosen) (engineeringCapability chosen)

Require functional capability grounds for the same chosen process and claim.

L388  implementationChoice : choiceSpecification chosenRequirements (chosenImplementation chosen) chosenReasons

Require reasoned choice of this chosen implementation under actual requirements and reasons.

L389  ownClaimGrounds : ∀ fact, inferentialSpecification (ownFactPremises chosen) (ownFactClaim chosen fact)

For all own facts, require inference from the chosen-identity premises to the exact fact claim.

L390  observedHere : Compatible [presentBudgetRecord] chosen

Require chosen itself to be compatible with the actual budget observation.

L391  selectionActuallyAdopted : (selectionPosition chosen).commitment chosen

Require the chosen selection commitment to be actually adopted at chosen.

L392  currentOwnClaims : Models (ownTheory chosen) chosen

Require chosen to model every held claim of the full combined theory.

L393  fullNormativeContents : ∀ norm, normApplies chosen norm →

For every applicable norm, require actual theory membership of its content.

L394    ownTheory chosen (ownNormClaim chosen norm)

The held content must be that same norm's complete ownNormClaim.

L395  wholeClaimGrounds : ∀ claim, ownTheory chosen claim →

For every actual held claim, require its inferential grounds.

L396    inferentialSpecification (ownFactPremises chosen) claim

Those grounds retain the explicit chosen-identity assumptions.

L398theorem inheritedCurrent (chosen : Candidate)

Construct all Inherited fields for a selected design.

L399    (ordinary : chosen = .presentSimple ∨ chosen = .evolvable) :

Assume it is presentSimple or evolvable.

L400    Inherited sharedContext chosen := by

The resulting bundle is in exactly sharedContext.

L401  refine ⟨rfl, engineeringGenerative, currentConsistency chosen ordinary,

Supply context identity, actual generation proof and full current consistency.

L402    currentSelfApplication chosen ordinary, governanceGrounded,

Supply actual self-application and grounds for every governance principle.

L403    selectionGrounded chosen ordinary, grounds012Singleton _ budgetEmpiricalDischarged,

Supply chosen selection grounds and the discharged empirical singleton task.

L404    grounds012Singleton _ budgetInferentialDischarged, budgetScopeExplained,

Supply discharged capacity inference and the actual scope account.

L405    engineeringCapabilityGrounded chosen, ?_, actualOwnFactGrounded chosen ordinary,

Supply capability grounds, leave implementation choice open, and supply all own-fact grounds.

L406    ?_, rfl, (currentAdmissible chosen ordinary).1,

Leave observation compatibility open; supply adoption identity and actual full-theory satisfaction.

L407    allNormativeContentHeld chosen, wholeClaimGrounded chosen ordinary⟩

Supply applicable normative membership and grounds for every held claim.

L408  · apply implementationReasoned

For the implementation field, apply the actual reasoned-choice theorem.

L409    rcases ordinary with rfl | rfl <;> change _ ≤ 12 <;> decide

Split ordinary choices and compute the remaining ≤ 12 budget condition.

L410  · apply (budgetObservationMeaning _).2

For observation compatibility, use the backward budget observation equivalence.

L411    rcases ordinary with rfl | rfl <;> change _ ≤ 3 <;> decide

Split ordinary choices and compute their ≤ 3 observation bound.

L413/- Mutual application extracts duties for the same system, principles, claims

Comment introduces mutual application to the same system, principles and claims.

L414and actual chosen implementation. It retains the full Inherited premise. -/

Comment includes the actual chosen implementation and retains the complete Inherited premise.

L415/-- organon-map CoreReader.Engineering.inheritedMutualApplication

Begin source-trace metadata for CoreReader.Engineering.inheritedMutualApplication; the following source identifiers and hashes are not Lean proof premises.

L416organon.relationships.roles#p1 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source unit organon.relationships.roles#p1 with SHA-256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L417organon.relationships.roles#p2 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source unit organon.relationships.roles#p2 with SHA-256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L418organon.relationships.roles#p3 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source unit organon.relationships.roles#p3 with SHA-256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L419-/

End the source-trace metadata comment; Lean does not elaborate it as a proof term.

L420theorem inheritedMutualApplication (ctx : Context) (chosen : Candidate)

For any ctx and chosen, inheritedMutualApplication extracts same-object obligations from Inherited.

L421    (inherited : Inherited ctx chosen) :

The full inherited bundle is an explicit premise, not the theorem's independently derived conclusion.

L422    generationSpecification engineeringPolicy ∧

Return the actual engineering generation specification.

L423    reflexivitySpecification (selfModel chosen).rules (selfModel chosen).self

Return reflexivity on the chosen model's rules and self relation.

L424      (selfModel chosen).performed ∧

Retain that same model's performance relation.

L425    (∀ principle, valueSpecification (governancePosition principle)) ∧

Return value grounds universally over all Core principles.

L426    capabilitySpecification (engineeringProcess chosen) (engineeringCapability chosen) ∧

Return capability grounds for the chosen process and its exact claim.

L427    choiceSpecification chosenRequirements (chosenImplementation chosen) chosenReasons ∧

Return actual reasoned implementation choice.

L428    (∀ fact, inferentialSpecification (ownFactPremises chosen) (ownFactClaim chosen fact)) ∧

Return inference grounds for every own fact under chosen-identity premises.

L429    (∀ norm, normApplies chosen norm → ownTheory chosen (ownNormClaim chosen norm)) ∧

Return theory membership of every norm whose applicability premise holds.

L430    (∀ claim, ownTheory chosen claim → inferentialSpecification (ownFactPremises chosen) claim) ∧

Return inferential grounds for every claim actually held in the combined theory.

L431    consistencySpecification (engineeringSnapshot .evolvable 0)

Return current full-theory consistency and truthful change reporting against the earlier evolvable snapshot.

L432      (engineeringSnapshot chosen 1) true :=

Its current side remains chosen revision 1 with change recorded true.

L433  ⟨inherited.generation, inherited.reflection, inherited.ownPrincipleGrounds,

Build the conjunction by projecting generation, reflection and governance grounds from inherited.

L434    inherited.capabilityGrounds, inherited.implementationChoice, inherited.ownClaimGrounds,

Project capability, actual implementation choice and own-fact grounds.

L435    inherited.fullNormativeContents, inherited.wholeClaimGrounds, inherited.consistency⟩

Project full normative membership, all-held-claim grounds and full consistency; no extra proof of their premises occurs here.

L437/-- organon-map CoreReader.Engineering.inheritedMutualCases

Begin source-trace metadata for CoreReader.Engineering.inheritedMutualCases; the following source identifiers and hashes are not Lean proof premises.

L438organon.relationships.roles#p1 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source unit organon.relationships.roles#p1 with SHA-256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L439organon.relationships.roles#p2 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source unit organon.relationships.roles#p2 with SHA-256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L440organon.relationships.roles#p3 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source unit organon.relationships.roles#p3 with SHA-256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L441-/

End the source-trace metadata comment; Lean does not elaborate it as a proof term.

L442theorem inheritedMutualCases :

inheritedMutualCases gives concrete positive duties alongside actual self-criticism results.

L443    Inherited sharedContext .evolvable ∧

The full Inherited bundle holds for evolvable in sharedContext.

L444    valueSpecification (governancePosition .grounds) ∧

The grounds principle's governance value specification holds.

L445    capabilitySpecification (engineeringProcess .evolvable) (engineeringCapability .evolvable) ∧

The actual evolvable process has its exact functional capability grounds.

L446    choiceSpecification chosenRequirements (chosenImplementation .evolvable) chosenReasons ∧

The evolvable implementation has actual reasoned-choice support.

L447    Reflection.evaluate ((selfModel .evolvable).input ⟨0, .evolutionMethod, .revision⟩) = .counterexample ∧

The actual batch-method revision evaluates to counterexample.

L448    (.generationRule : ReviewObject) ∈ (selfModel .evolvable).objects ∧

The generationRule object actually belongs to the evolvable model.

L449    (.assessmentRule : ReviewObject) ∈ (selfModel .evolvable).objects ∧

The assessmentRule object belongs to that same model.

L450    Reflection.evaluate ((selfModel .evolvable).input ⟨0, .assessmentRule, .revision⟩) = .counterexample :=

The actual assessment-rule revision also evaluates to counterexample.

L451  ⟨inheritedCurrent .evolvable (Or.inr rfl), governanceGrounded .grounds,

Use the full inheritedCurrent witness and actual grounds-principle value theorem.

L452    engineeringCapabilityGrounded .evolvable,

Use the exact evolvable capability-grounding theorem.

L453    (inheritedCurrent .evolvable (Or.inr rfl)).implementationChoice,

Extract reasoned implementation choice from that same inherited witness.

L454    (actualSelfCriticism .evolvable).2.2.1,

Extract the batch-method counterexample from actualSelfCriticism.

L455    (ownRuleIdentity .evolvable .generation .revision).1,

Extract generation-rule object membership from ownRuleIdentity.

L456    (ownRuleIdentity .evolvable .assessment .revision).1,

Extract assessment-rule object membership from the corresponding identity theorem.

L457    (ownRuleContentVariation .evolvable).2.2.2.2.1⟩

Extract the current assessment-rule revision counterexample from ownRuleContentVariation.

L459/- In the adopter's same context, the actual priority object and its own

Comment locates the priority object and its assessment method in the adopter's same context.

L460assessment method remain within the inherited criticism/generation contract. -/

Comment retains both objects within the inherited criticism/generation contract.

L461/-- organon-map CoreReader.Engineering.priorityRemainsReflexive

Begin source-trace metadata for CoreReader.Engineering.priorityRemainsReflexive; the following source identifiers and hashes are not Lean proof premises.

L462organon.relationships.roles#p3 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source unit organon.relationships.roles#p3 with SHA-256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L463extensions#p1 sha256 ec87a2f17b2f88addcadea0108add11ad3d4239daf56db466ba0ddbe7cc92b66

Record source unit extensions#p1 with SHA-256 ec87a2f17b2f88addcadea0108add11ad3d4239daf56db466ba0ddbe7cc92b66; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L464software-engineering.structural-judgment#p1 sha256 8014457feae3410a7220426dbbe4293f7b5d1d2aa152f4085ccd1f03d5983a42

Record source unit software-engineering.structural-judgment#p1 with SHA-256 8014457feae3410a7220426dbbe4293f7b5d1d2aa152f4085ccd1f03d5983a42; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L465software-engineering.revision#p2 sha256 5d31bed0197ea7e7028eb7a85e56059516421c6c27613cc5479e0b98c5111d99

Record source unit software-engineering.revision#p2 with SHA-256 5d31bed0197ea7e7028eb7a85e56059516421c6c27613cc5479e0b98c5111d99; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L466-/

End the source-trace metadata comment; Lean does not elaborate it as a proof term.

L467theorem priorityRemainsReflexive (ctx : Context) (chosen : Candidate)

priorityRemainsReflexive connects domain priority to inherited self-criticism in an explicit context and choice.

L468    (inherited : Inherited ctx chosen) (domain : DomainSatisfied ctx chosen)

Assume the complete Inherited bundle and actual DomainSatisfied for the same ctx/chosen.

L469    (applicable : PriorityConditions ctx) (noDeparture : ¬ JustifiedDeparture ctx .evolvable) :

Also assume priority applies and evolvable has no justified departure in that same context.

L470    chosen = .evolvable ∧

Conclude the selected candidate must be evolvable.

L471    (.priority : ReviewObject) ∈ (selfModel chosen).objects ∧

Its actual priority object belongs to its self-review list.

L472    reflexivitySpecification (selfModel chosen).rules (selfModel chosen).self

The chosen self-model still satisfies reflexivity over its actual rules and targets.

L473      (selfModel chosen).performed ∧

Retain its actual performance relation in that specification.

L474    (∀ principle, valueSpecification (governancePosition principle)) ∧

Retain value grounds for every inherited Core principle.

L475    Grounds012 (EvolutionPriority ctx) canonicalArticulation

Additionally ground the actual EvolutionPriority ctx claim, with canonical articulation.

L476      [.value (selectionPosition .evolvable)] (.value (selectionPosition .evolvable)) ∧

Its required and supplied facet are the very same evolvable selection value position.

L477    ownTheory chosen (ownNormClaim chosen .domain) ∧

The full actual domain norm is held in chosen's combined theory.

L478    consistencySpecification (engineeringSnapshot .evolvable 0)

The full inherited consistency specification is retained.

L479      (engineeringSnapshot chosen 1) true := by

The current snapshot remains chosen revision 1, with acknowledged change true.

L480  have selected := (priorityWhenApplicable ctx chosen domain.2.1 applicable noDeparture).1

Extract actual priority from domain and apply applicability/noDeparture to derive chosen = evolvable.

L481  refine ⟨selected, ?_, inherited.reflection, inherited.ownPrincipleGrounds,

Construct the selected identity, leave membership open, and project reflection and Core value grounds.

L482    ?_, allNormativeContentHeld chosen .domain selected, inherited.consistency⟩

Leave exact-priority grounds open; use selected as domain norm applicability and project consistency.

L483  · subst chosen; decide

Replace chosen with evolvable and compute actual priority-object membership.

L484  · rw [inherited.sameContext]

Rewrite ctx to sharedContext using the Inherited identity field; this bounds the grounds result's context.

L485    exact priorityGrounds

Now apply priorityGrounds for the exact same priority predicate.

L487/-- organon-map CoreReader.Engineering.priorityReflexiveCases

Begin source-trace metadata for CoreReader.Engineering.priorityReflexiveCases; the following source identifiers and hashes are not Lean proof premises.

L488organon.relationships.roles#p3 sha256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e

Record source unit organon.relationships.roles#p3 with SHA-256 24b533c77fe93d0570da65ee361893f2c445842f48ee6f315f99f8abc06a0e5e; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L489extensions#p1 sha256 ec87a2f17b2f88addcadea0108add11ad3d4239daf56db466ba0ddbe7cc92b66

Record source unit extensions#p1 with SHA-256 ec87a2f17b2f88addcadea0108add11ad3d4239daf56db466ba0ddbe7cc92b66; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L490software-engineering.structural-judgment#p1 sha256 8014457feae3410a7220426dbbe4293f7b5d1d2aa152f4085ccd1f03d5983a42

Record source unit software-engineering.structural-judgment#p1 with SHA-256 8014457feae3410a7220426dbbe4293f7b5d1d2aa152f4085ccd1f03d5983a42; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L491software-engineering.revision#p2 sha256 5d31bed0197ea7e7028eb7a85e56059516421c6c27613cc5479e0b98c5111d99

Record source unit software-engineering.revision#p2 with SHA-256 5d31bed0197ea7e7028eb7a85e56059516421c6c27613cc5479e0b98c5111d99; this comment tracks the reviewed source object, not a logical assumption or correspondence proof.

L492-/

End the source-trace metadata comment; Lean does not elaborate it as a proof term.

L493theorem priorityReflexiveCases :

priorityReflexiveCases computes actual priority review and retains criticisms of distinct method objects.

L494    (.priority : ReviewObject) ∈ (selfModel .evolvable).objects ∧

The priority object is actually listed for evolvable.

L495    objectTest .priority (.evolvable, 10) = true ∧

Its finite size-10 object test passes.

L496    (selfModel .evolvable).performed ⟨0, 1⟩ ⟨0, .priority, .revision⟩

The model records actual performance under assessment key (0,1) for priority revision owned by 0.

L497      ((selfModel .evolvable).input ⟨0, .priority, .revision⟩)

The performed input is exactly the input built for that same target.

L498      (.assessed .supportedWithinScope) ∧

The recorded outcome is assessed supportedWithinScope.

L499    Reflection.evaluate ((selfModel .evolvable).input ⟨0, .evolutionMethod, .revision⟩) = .counterexample ∧

The distinct batch-method revision nevertheless yields counterexample.

L500    objectTest .evolutionMethod (.evolvable, 10) = true ∧

The old batch-method size-10 test succeeds.

L501    objectTest .evolutionMethod (.evolvable, 5) = false ∧

The challenged size-5 test fails.

L502    Grounds012 (EvolutionPriority sharedContext) canonicalArticulation

Keep grounds for actual priority in sharedContext with canonical articulation.

L503      [.value (selectionPosition .evolvable)] (.value (selectionPosition .evolvable)) ∧

Use its identical singleton required/supplied evolvable value facet.

L504    Reflection.evaluate ((selfModel .evolvable).input ⟨0, .assessmentRule, .revision⟩) = .counterexample := by

The assessment-rule revision's local-contract failure is also retained as a counterexample.

L505  refine ⟨by decide, by decide, ?_, (actualSelfCriticism .evolvable).2.2.1,

Compute priority membership and test success; leave performed, while extracting batch criticism.

L506    (actualSelfCriticism .evolvable).1, (actualSelfCriticism .evolvable).2.1,

Extract the batch method's old success and challenged failure.

L507    priorityGrounds, (ownRuleContentVariation .evolvable).2.2.2.2.1⟩

Supply actual priority grounds and the actual rule-revision counterexample.

L508  exact ⟨⟨rfl, by decide⟩, rfl, .assessment, rfl, rfl⟩

Construct performed from self membership, exact input and the assessment activity's key/record identities.

L510/- The witness is nonempty and satisfies the entire represented inherited and

Comment introduces a nonempty witness satisfying the entire represented inherited bundle.

L511domain bundles in the very same continuing activity, with active priority. -/

Comment also requires the domain bundle in the very same continuing activity with active priority.

L512/-- organon-map CoreReader.Engineering.jointWitness

Begin source-trace metadata for CoreReader.Engineering.jointWitness; the following source identifiers and hashes are not Lean proof premises.

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L556-/

End the source-trace metadata comment; Lean does not elaborate it as a proof term.

L557theorem jointWitness :

jointWitness exhibits one nonempty finite model jointly satisfying inherited and domain bundles.

L558    ∃ ctx : Context, ∃ chosen : Candidate,

Existentially choose a context and Candidate; this is an existence result, not universal adequacy.

L559      ctx = sharedContext ∧ chosen = .evolvable ∧

Require the witnesses to be exactly sharedContext and evolvable.

L560      Inherited ctx chosen ∧ DomainSatisfied ctx chosen ∧

Both complete bundles must hold for these same objects.

L561      PriorityConditions ctx ∧ ¬ HasThreat ctx .evolvable ∧

Priority applicability is active and evolvable has no represented threat.

L562      abstractionComplexity .presentSimple < abstractionComplexity chosen ∧

The chosen design has greater abstraction complexity than presentSimple.

L563      CanChange ctx.activity chosen .successor .designRevision ∧

The successor has an actual designRevision path in that same activity/design.

L564      CanChange ctx.activity chosen .agent .designRevision ∧

The agent has an actual designRevision path there too.

L565      ownTheory chosen (ownFactClaim chosen .selected) ∧

The selected-design report is actually held in chosen's theory.

L566      (.commitment .grounds : ReviewObject) ∈ (selfModel chosen).objects ∧

The grounds commitment is actually among chosen's self-review objects.

L567      Admissible (ownTheory chosen) (comparisonContext chosen) chosen := by

Chosen is an admissible model of its full combined theory and comparison context.

L568  exact ⟨sharedContext, .evolvable, rfl, rfl,

Choose sharedContext and evolvable as witnesses, proving both identity fields reflexively.

L569    inheritedCurrent .evolvable (Or.inr rfl), currentDomainSatisfied,

Supply the complete inheritedCurrent bundle and currentDomainSatisfied.

L570    currentPriorityConditions, currentNoThreat.1, by decide, by decide, by decide,

Supply active priority/no threat, then compute complexity ordering and both maintainer paths.

L571    (nonemptyOwnObjects .evolvable).1, (nonemptyOwnObjects .evolvable).2.2.2,

Project held selection and the actual grounds-review object from nonemptyOwnObjects.

L572    currentAdmissible .evolvable (Or.inr rfl)⟩

Finish with the actual full-theory admissibility proof.

L574/- The countermodel adopts a supported present-simplicity value and actually

Comment introduces a countermodel adopting the supported present-simplicity value.

L575chooses that option. Every inherited duty still holds. The domain conditions

Comment states actual selection and full inherited satisfaction while beginning the applicability qualification.

L576are active; neither lifecycle nor threatened costs supplies an escape. -/

Comment rules out inactive domain conditions, bounded lifecycle and threatened costs as escape explanations.

L577/-- organon-map CoreReader.Engineering.inheritedDoesNotEntailPriority

Begin source-trace metadata for CoreReader.Engineering.inheritedDoesNotEntailPriority; the following source identifiers and hashes are not Lean proof premises.

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L583software-engineering.evolution-priority#p2 sha256 c2237515e869b2f88269cf19e3c97ef80c3c87342d1a03cd911cac03fe5a3a04

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L584software-engineering.evolution-priority#p3 sha256 c2237515e869b2f88269cf19e3c97ef80c3c87342d1a03cd911cac03fe5a3a04

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L585-/

End the source-trace metadata comment; Lean does not elaborate it as a proof term.

L586theorem inheritedDoesNotEntailPriority :

inheritedDoesNotEntailPriority exhibits a finite countermodel separating inherited duties from the additional priority adoption.

L587    ∃ ctx : Context, ∃ chosen : Candidate,

Existentially choose a context and candidate satisfying all following conjuncts.

L588      ctx = sharedContext ∧ chosen = .presentSimple ∧

Fix them to sharedContext and presentSimple.

L589      Inherited ctx chosen ∧ PriorityConditions ctx ∧

The full inherited bundle holds while the domain priority conditions are active.

L590      Continuing ctx.activity ∧ ¬ BoundedLifecycle ctx.activity ∧

The same activity is continuing and has no bounded lifecycle.

L591      ¬ HasThreat ctx .evolvable ∧ ¬ JustifiedDeparture ctx .evolvable ∧

There is neither a threat nor a justified departure for evolvable.

L592      Meets ctx.required (ctx.profiles .presentSimple) ∧

presentSimple meets the actual necessary requirements.

L593      Meets ctx.required (ctx.profiles .evolvable) ∧

evolvable also meets those same requirements.

L594      credible ctx.evidence .designRevision ∧

The same evidence makes designRevision credible.

L595      CanChange ctx.activity .evolvable .successor .designRevision ∧

The successor can revise evolvable in this activity.

L596      CanChange ctx.activity .evolvable .agent .designRevision ∧

The agent can revise evolvable there too.

L597      changeWork .evolvable .designRevision < changeWork chosen .designRevision ∧

evolvable requires less actual design-revision work than chosen presentSimple.

L598      abstractionComplexity chosen < abstractionComplexity .evolvable ∧

Chosen presentSimple has less present abstraction complexity than evolvable.

L599      valueSpecification (selectionPosition chosen) ∧

The chosen simplicity value position has its actual value grounds.

L600      (selectionPosition chosen).commitment chosen ∧

The same value position is actually committed to the chosen design.

L601      ¬ EvolutionPriority ctx chosen := by

Nevertheless the actual EvolutionPriority claim is false for that choice.

L602  exact ⟨sharedContext, .presentSimple, rfl, rfl,

Choose sharedContext and presentSimple, discharging their identities reflexively.

L603    inheritedCurrent .presentSimple (Or.inl rfl), currentPriorityConditions,

Provide complete inherited satisfaction and active priority conditions.

L604    by decide, by decide, currentNoThreat.1, currentNoThreat.2,

Compute continuation and unboundedness, then use both no-threat/no-departure facts.

L605    by decide, by decide, by decide, by decide, by decide, by decide, by decide,

Compute both requirements, credible revision, both maintainer paths, and the work/complexity inequalities.

L606    selectionGrounded .presentSimple (Or.inl rfl), rfl, currentSimpleViolates⟩

Use actual simple-position grounds, reflexive adoption and currentSimpleViolates to finish the countermodel.

L608end CoreReader.Engineering

Close namespace CoreReader.Engineering; no further mathematical claim is asserted.