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theorem proved term proof

interpret_eq_parity

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formal statement (Lean)

 255theorem interpret_eq_parity (n : LogicNat) :
 256    StrictLogicRealization.interpret strictBooleanRealization n =
 257      Nat.bodd (LogicNat.toNat n) := by

proof body

Term-mode proof.

 258  induction n with
 259  | identity => rfl
 260  | step n ih =>
 261      show xorBool true (StrictLogicRealization.interpret strictBooleanRealization n) =
 262        Nat.bodd (Nat.succ (LogicNat.toNat n))
 263      rw [xorBool_true, ih, Nat.bodd_succ]
 264
 265/-- Even though the carrier image collapses, the iteration object is the
 266full `LogicNat`. Concretely: the interpretation map is not injective. -/

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