`modularRealization`

definition

show as: view math explainer →

module: IndisputableMonolith.Foundation.ModularLogicRealization
domain: Foundation
line: 67 · github
papers citing: none yet

open explainer

Generate a durable explainer page for this declaration.

open lean source

IndisputableMonolith.Foundation.ModularLogicRealization on GitHub at line 67.

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

  64  simpa [Nat.mod_eq_of_lt (one_lt_modulus k)] using h
  65
  66/-- Finite cyclic Law-of-Logic realization with periodic interpretation. -/
  67def modularRealization (k : ℕ) : LogicRealization where
  68  Carrier := Fin (modulus k)
  69  Cost := Nat
  70  zeroCost := inferInstance
  71  compare := finCost
  72  zero := ⟨0, modulus_pos k⟩
  73  step := cycStep k
  74  Orbit := ArithmeticFromLogic.LogicNat
  75  orbitZero := ArithmeticFromLogic.LogicNat.zero
  76  orbitStep := ArithmeticFromLogic.LogicNat.succ
  77  interpret := modularInterpret k
  78  interpret_zero := modularInterpret_zero k
  79  interpret_step := modularInterpret_step k
  80  orbit_no_confusion := by
  81    intro n h
  82    exact ArithmeticFromLogic.LogicNat.zero_ne_succ n h
  83  orbit_step_injective := ArithmeticFromLogic.LogicNat.succ_injective
  84  orbit_induction := by
  85    intro P h0 hs n
  86    exact ArithmeticFromLogic.LogicNat.induction (motive := P) h0 hs n
  87  orbitEquivLogicNat := Equiv.refl ArithmeticFromLogic.LogicNat
  88  orbitEquiv_zero := rfl
  89  orbitEquiv_step := by intro n; rfl
  90  identity := finCost_self
  91  nonContradiction := finCost_symm
  92  excludedMiddle := True
  93  composition := True
  94  actionInvariant := True
  95  nontrivial := by
  96    refine ⟨⟨1, one_lt_modulus k⟩, ?_⟩
  97    simp [finCost]

papers checked against this theorem

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