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refactor: correct para_open_out variable orientation #920

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refactor: correct para_open_out variable orientation #920

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4 changes: 2 additions & 2 deletions Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/FullBetaConfluence.lean
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Expand Up @@ -132,8 +132,8 @@ lemma para_open_close (x y z) (para : M ⭢ₚ M') : M⟦z ↜ x⟧⟦z ↝ fvar
by grind

/-- Parallel substitution respects fresh opening. -/
lemma para_open_out (L : Finset Var) (mem : ∀ x, x ∉ L → (M ^ fvar x) ⭢ₚ N ^ fvar x)
(para : M' ⭢ₚ N') : (M ^ M') ⭢ₚ (N ^ N') := by
lemma para_open_out (L : Finset Var) (mem : ∀ x, x ∉ L → (M ^ fvar x) ⭢ₚ M' ^ fvar x)
(para : N ⭢ₚ N') : (M ^ N) ⭢ₚ (M' ^ N') := by
grind [fresh_exists <| free_union [fv] Var]

-- TODO: the Takahashi translation would be a much nicer and shorter proof, but I had difficultly
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