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def definition def or abbrev

ethicsRealization

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formal statement (Lean)

  38def ethicsRealization : LogicRealization where
  39  Carrier := MoralImprovementStep

proof body

Definition body.

  40  Cost := Nat
  41  zeroCost := inferInstance
  42  compare := ethicsCost
  43  zero := 0
  44  step := Nat.succ
  45  Orbit := LogicNat
  46  orbitZero := LogicNat.zero
  47  orbitStep := LogicNat.succ
  48  interpret := ethicsInterpret
  49  interpret_zero := by rfl
  50  interpret_step := by
  51    intro n
  52    show LogicNat.toNat (LogicNat.succ n) = Nat.succ (LogicNat.toNat n)
  53    rfl
  54  orbit_no_confusion := by intro n h; exact LogicNat.zero_ne_succ n h
  55  orbit_step_injective := LogicNat.succ_injective
  56  orbit_induction := by
  57    intro P h0 hs n
  58    exact LogicNat.induction (motive := P) h0 hs n
  59  orbitEquivLogicNat := Equiv.refl LogicNat
  60  orbitEquiv_zero := rfl
  61  orbitEquiv_step := by intro n; rfl
  62  identity := ethicsCost_self
  63  nonContradiction := ethicsCost_symm
  64  excludedMiddle := True
  65  composition := True
  66  actionInvariant := True
  67  nontrivial := by
  68    refine ⟨1, ?_⟩
  69    simp [ethicsCost]
  70

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