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theorem proved term proof

distinctionInterpret_step

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formal statement (Lean)

  82@[simp] theorem distinctionInterpret_step {K : Type u} (x y : K)
  83    (n : ULift.{u} LogicNat) :
  84    distinctionInterpret x y (ULift.up (LogicNat.step n.down)) =
  85      distinctionStep x y (distinctionInterpret x y n) := by

proof body

Term-mode proof.

  86  cases n with
  87  | up n =>
  88    cases n <;> rfl
  89
  90/-- **Universal instantiation theorem.**
  91
  92Any carrier with a named distinction `x ≠ y` is a `LogicRealization` on
  93that very carrier. -/

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