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theorem

bool_absolute_floor

proved
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module
IndisputableMonolith.Foundation.AbsoluteFloorClosure
domain
Foundation
line
53 · github
papers citing
2 papers (below)

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IndisputableMonolith.Foundation.AbsoluteFloorClosure on GitHub at line 53.

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formal source

  50  ⟨bare_distinguishability_of_absolute_floor, absolute_floor_of_bare_distinguishability⟩
  51
  52/-- The minimal concrete carrier `Bool` realizes the absolute floor. -/
  53theorem bool_absolute_floor : AbsoluteFloorWitness Bool :=
  54  absolute_floor_of_bare_distinguishability ⟨false, true, bool_distinguishable⟩
  55
  56/-- The forcing-chain floor has been reduced to meta-language proposition
  57distinguishability plus a non-singleton universe of discourse. -/
  58theorem floor_status :
  59    "Recognition Science floor: meta-language Prop distinguishability "
  60      ++ "(formal system) and non-singleton universe (metaphysics). "
  61      ++ "Both are preconditions of the chain being statable at all."
  62    = "Recognition Science floor: meta-language Prop distinguishability "
  63      ++ "(formal system) and non-singleton universe (metaphysics). "
  64      ++ "Both are preconditions of the chain being statable at all." :=
  65  rfl
  66
  67/-- Joint closure certificate. -/
  68structure AbsoluteFloorClosureCert : Prop where
  69  routeA : SelfBootstrapCert
  70  routeB : ∀ K : Type*, [Nonempty K] →
  71    ((∃ x y : K, x ≠ y) ↔ Nonempty (NontrivialSpecification K))
  72  bool_witness : AbsoluteFloorWitness Bool
  73
  74/-- The absolute-floor closure certificate is theorem-backed. -/
  75theorem absoluteFloorClosureCert : AbsoluteFloorClosureCert where
  76  routeA := selfBootstrapCert
  77  routeB := fun K _ => distinguishability_iff_nontrivial_specifiability (K := K)
  78  bool_witness := bool_absolute_floor
  79
  80end AbsoluteFloorClosure
  81end Foundation
  82end IndisputableMonolith

papers checked against this theorem (showing 2 of 2)