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refactor(LocallyNameless/Untyped): rename close_open => close_openRec #678

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refactor(LocallyNameless/Untyped): rename close_open => close_openRec #678

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6 changes: 5 additions & 1 deletion Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/Properties.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -151,9 +151,13 @@ lemma close_open_to_subst (m n : Term Var) (x : Var) (m_lc : LC m) (n_lc : LC n)
(m ^* x) ^ n = m [x := n] := close_openRec_to_subst m n x 0 m_lc n_lc

/-- Closing and opening are inverses. -/
lemma close_open (x : Var) (t : Term Var) (k : ℕ) (t_lc : LC t) : t⟦k ↜ x⟧⟦k ↝ fvar x⟧ = t := by
lemma close_openRec (x : Var) (t : Term Var) (k : ℕ) (t_lc : LC t) : t⟦k ↜ x⟧⟦k ↝ fvar x⟧ = t := by
grind [subst_refl]

/-- Closing and opening are inverses. -/
lemma close_open (x : Var) (t : Term Var) (t_lc : LC t) : (t ^* x) ^ fvar x = t :=
close_openRec x t 0 t_lc

end LambdaCalculus.LocallyNameless.Untyped.Term

end Cslib
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