`RecognitionStructure`

definition

show as: view math explainer →

module: IndisputableMonolith.Recognition
domain: Recognition
line: 31 · github
papers citing: none yet

open explainer

Generate a durable explainer page for this declaration.

open lean source

IndisputableMonolith.Recognition on GitHub at line 31.

browse module

All declarations in this module, on Recognition.

explainer page

Tracked in the explainer inventory; generation is lazy so crawlers do not trigger LLM jobs.

open explainer

depends on

used by

formal source

  28theorem nothing_cannot_recognize_itself : NothingCannotRecognizeItself :=
  29  mp_holds
  30
  31structure RecognitionStructure where
  32  U : Type
  33  R : U → U → Prop
  34
  35structure Chain (M : RecognitionStructure) where
  36  n : Nat
  37  f : Fin (n+1) → M.U
  38  ok : ∀ i : Fin n, M.R (f i.castSucc) (f i.succ)
  39
  40namespace Chain
  41variable {M : RecognitionStructure} (ch : Chain M)
  42def head : M.U := by
  43  have hpos : 0 < ch.n + 1 := Nat.succ_pos _
  44  exact ch.f ⟨0, hpos⟩
  45def last : M.U := by
  46  have hlt : ch.n < ch.n + 1 := Nat.lt_succ_self _
  47  exact ch.f ⟨ch.n, hlt⟩
  48end Chain
  49
  50structure Ledger (M : RecognitionStructure) where
  51  debit : M.U → ℤ
  52  credit : M.U → ℤ
  53
  54@[simp] def Ledger.Carrier {M : RecognitionStructure} (_ : Ledger M) : Type :=
  55  M.U
  56
  57def phi {M} (L : Ledger M) : M.U → ℤ := fun u => L.debit u - L.credit u
  58
  59def chainFlux {M} (L : Ledger M) (ch : Chain M) : ℤ :=
  60  phi L (Chain.last ch) - phi L (Chain.head ch)
  61

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.