Skip to content

feat: remove open_fresh_preserve_not_fvar #573

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
chenson2018 merged 1 commit into from
May 20, 2026
Merged

feat: remove open_fresh_preserve_not_fvar #573

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
2 changes: 1 addition & 1 deletion Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/FullBeta.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -104,7 +104,7 @@ lemma step_not_fv (step : M ⭢βᶠ N) (hw : w ∉ M.fv) : w ∉ N.fv := by
| abs =>
have ⟨x, _⟩ := fresh_exists <| free_union [fv] Var
have := open_close x
grind [close_preserve_not_fvar, open_fresh_preserve_not_fvar]
grind [close_preserve_not_fvar, open_preserve_not_fvar]
| _ => grind

/-- Abstracting then closing preserves a single reduction. -/
Expand Down
2 changes: 1 addition & 1 deletion Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/FullEta.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -69,7 +69,7 @@ lemma step_not_fv (step : M ⭢ηᶠ M') (hw : w ∉ M.fv) : w ∉ M'.fv := by
| abs =>
have ⟨x, _⟩ := fresh_exists <| free_union [fv] Var
have := open_close x
grind [close_preserve_not_fvar, open_fresh_preserve_not_fvar]
grind [close_preserve_not_fvar, open_preserve_not_fvar]
| _ => grind

/-- Substitution of a fresh variable preserves an η-reduction step. -/
Expand Down
7 changes: 1 addition & 6 deletions Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/Properties.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -55,11 +55,6 @@ lemma swap_open_fvar_close (k n : ℕ) (x y : Var) (m : Term Var) (neq₁ : k
lemma close_preserve_not_fvar {k x y} (m : Term Var) (nmem : x ∉ m.fv) : x ∉ (m⟦k ↜ y⟧).fv := by
induction m generalizing k <;> grind

/-- Opening to a fresh free variable preserves free variables. -/
lemma open_fresh_preserve_not_fvar {k x y} (m : Term Var) (nmem : x ∉ m.fv) (neq : x ≠ y) :
x ∉ (m⟦k ↝ fvar y⟧).fv := by
induction m generalizing k <;> grind

/-- Opening preserves free variables. -/
lemma open_preserve_not_fvar {k x} (m n : Term Var) (nmem_m : x ∉ m.fv) (nmem_n : x ∉ n.fv) :
x ∉ (m⟦k ↝ n⟧).fv := by
Expand Down Expand Up @@ -144,7 +139,7 @@ lemma open_close_to_subst (m : Term Var) (x y : Var) (k : ℕ) (m_lc : LC m) :
grind [
swap_open, =_ swap_open_fvar_close,
open_close x' (t⟦k+1 ↜ x⟧⟦k+1 ↝ fvar y⟧) 0, open_close x' (t[x := fvar y]) 0,
open_fresh_preserve_not_fvar, close_preserve_not_fvar, subst_preserve_not_fvar]
open_preserve_not_fvar, close_preserve_not_fvar, subst_preserve_not_fvar]
| _ => grind

/-- Closing and opening are inverses. -/
Expand Down
Loading