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refactor: Replace ↔ with = in LcAt.lean #787

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refactor: Replace ↔ with = in LcAt.lean #787

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4 changes: 2 additions & 2 deletions Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/LcAt.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -67,11 +67,11 @@ theorem depth_open_fvar_eq_depth (M : Term Var) (x : Var) : depth (M ^ fvar x) =
/-- Opening for some free variable at i-th bound variable, increments `LcAt`. -/
@[simp, scoped grind =]
theorem lcAt_openRec_fvar_iff_lcAt (M : Term Var) (x : Var) (i : ℕ) :
LcAt i (M⟦i ↝ fvar x⟧) ↔ LcAt (i + 1) M := by
LcAt i (M⟦i ↝ fvar x⟧) = LcAt (i + 1) M := by
induction M generalizing i <;> grind

/-- Opening for some free variable is locally closed if and only if `M` is `LcAt 1`. -/
theorem lcAt_open_fvar_iff_lcAt (M : Term Var) (x : Var) : LcAt 0 (M ^ fvar x) ↔ LcAt 1 M :=
theorem lcAt_open_fvar_iff_lcAt (M : Term Var) (x : Var) : LcAt 0 (M ^ fvar x) = LcAt 1 M :=
lcAt_openRec_fvar_iff_lcAt M x 0

/-- Locally closed terms. -/
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