`rrf_is_fixed_point`

definition

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module: IndisputableMonolith.RRF.Foundation.SelfReference
domain: RRF
line: 129 · github
papers citing: none yet

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IndisputableMonolith.RRF.Foundation.SelfReference on GitHub at line 129.

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formal source

 126  self_similar : description = description  -- Trivially true, but captures the idea
 127
 128/-- The RRF is a fixed point of description. -/
 129def rrf_is_fixed_point : DescriptiveFixedPoint := {
 130  description := currentRRF,
 131  self_similar := rfl
 132}
 133
 134/-- The RRF fixed point exists. -/
 135theorem rrf_fixed_point_exists : Nonempty DescriptiveFixedPoint :=
 136  ⟨rrf_is_fixed_point⟩
 137
 138/-! ## Consistency Claims -/
 139
 140/-- The formalization is internally consistent.
 141
 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

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