`toLightweight`

definition

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module: IndisputableMonolith.Foundation.UniversalForcing.StrictRealization
domain: Foundation
line: 63 · github
papers citing: none yet

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IndisputableMonolith.Foundation.UniversalForcing.StrictRealization on GitHub at line 63.

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formal source

  60
  61/-- Convert a strict realization to the existing lightweight interface.
  62The orbit fields are all derived from `LogicNat`, not supplied by the caller. -/
  63def toLightweight (R : StrictLogicRealization) : LogicRealization where
  64  Carrier := R.Carrier
  65  Cost := R.Cost
  66  zeroCost := R.zeroCost
  67  compare := R.compare
  68  zero := R.one
  69  step := fun x => R.compose R.generator x
  70  Orbit := FreeOrbit R
  71  orbitZero := LogicNat.zero
  72  orbitStep := LogicNat.succ
  73  interpret := interpret R
  74  interpret_zero := rfl
  75  interpret_step := by intro n; rfl
  76  orbit_no_confusion := by
  77    intro n h
  78    exact LogicNat.zero_ne_succ n h
  79  orbit_step_injective := LogicNat.succ_injective
  80  orbit_induction := by
  81    intro P h0 hs n
  82    exact LogicNat.induction (motive := P) h0 hs n
  83  orbitEquivLogicNat := Equiv.refl LogicNat
  84  orbitEquiv_zero := rfl
  85  orbitEquiv_step := by intro n; rfl
  86  identity := R.identity_law
  87  nonContradiction := R.non_contradiction_law
  88  excludedMiddle := R.excluded_middle_law
  89  composition := R.composition_law
  90  actionInvariant := R.invariance_law
  91  nontrivial := ⟨R.generator, R.nontrivial_law⟩
  92
  93/-- Strict forced arithmetic is the arithmetic extracted from the derived

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