`InternalConsistency`

definition

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module: IndisputableMonolith.RRF.Foundation.SelfReference
domain: RRF
line: 145 · github
papers citing: none yet

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IndisputableMonolith.RRF.Foundation.SelfReference on GitHub at line 145.

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formal source

 142This is witnessed by the fact that it compiles without contradiction.
 143We cannot prove this from within (Gödel), but we can assert it.
 144-/
 145structure InternalConsistency where
 146  /-- Derivable from foundational axioms only. -/
 147  foundational : Nonempty (ℝ → ℝ)
 148  /-- No obvious contradiction. -/
 149  not_obviously_false : ¬(0 = 1)
 150  /-- All proofs in this file are terminal (no holes). -/
 151  rigorous_proofs_only : Bool
 152
 153/-- The RRF formalization is internally consistent. -/
 154def rrf_internally_consistent : InternalConsistency := {
 155  foundational := ⟨IndisputableMonolith.Cost.Jcost⟩,
 156  not_obviously_false := by norm_num,
 157  rigorous_proofs_only := true
 158}
 159
 160
 161/-- Internal consistency is witnessed. -/
 162theorem internal_consistency_exists : Nonempty InternalConsistency :=
 163  ⟨rrf_internally_consistent⟩
 164
 165/-! ## The Compilation as Recognition -/
 166
 167/-- Compilation is a recognition event.
 168
 169When Lean type-checks this file, it is performing a recognition:
 170verifying that the propositions are consistent with the type theory.
 171-/
 172structure CompilationAsRecognition where
 173  /-- The code being compiled. -/
 174  code : LeanCode
 175  /-- Compilation succeeds. -/

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