Skip to content

feat(FullBeta, FullEta): generalize step_not_fv #579

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

Open
lengyijun wants to merge 2 commits into
base: main
Choose a base branch
from
+4 −4
Open

feat(FullBeta, FullEta): generalize step_not_fv #579

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
5a0079a
feat(Eta): stronger step_not_fv
lengyijun May 19, 2026
6002d76
feat(FullBeta): generalize step_not_fv
lengyijun May 20, 2026
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 @@ -98,7 +98,7 @@ lemma redex_subst_cong (s s' : Term Var) (x y : Var) (step : s ⭢βᶠ s') :
redex_subst_cong_lc _ _ _ _ step (.fvar y)

/-- An β-reduction step does not introduce new free variables. -/
lemma step_not_fv (step : M ⭢βᶠ N) (hw : w ∉ M.fv) : w ∉ N.fv := by
lemma step_not_fv (step : M ⭢βᶠ N) : N.fv ⊆ M.fv := by
induction step with
| base h => cases h with | beta => grind [open_preserve_not_fvar]
| abs =>
Expand Down
4 changes: 2 additions & 2 deletions Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/FullBetaEtaConfluence.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -77,9 +77,9 @@ lemma stronglyCommute_eta_beta : StronglyCommute (@FullEta Var) FullBeta := by
cases h_eta with | eta =>
have ⟨w, _⟩ := fresh_exists <| free_union [fv] Var
have st_beta_w : app y₁ (fvar w) ⭢βᶠ N ^ fvar w := by grind [st_body_beta w]
rcases invert_step_app_fvar st_beta_w with ⟨u', _, st_u⟩ | ⟨u1, _, _⟩
rcases invert_step_app_fvar st_beta_w with ⟨u', h, st_u⟩ | ⟨u1, _, _⟩
· use u'
grind [open_eq_app ?_ (step_not_fv st_u ?_)]
apply open_eq_app at h <;> grind [FullBeta.step_not_fv st_u]
· use abs u1
grind [open_injective w N u1]
case abs S ys st_body_eta =>
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 @@ -63,7 +63,7 @@ lemma invert_step_app_fvar (step : (app M (fvar x)) ⭢ηᶠ N) :
variable [HasFresh Var] [DecidableEq Var]

/-- An η-reduction step does not introduce new free variables. -/
lemma step_not_fv (step : M ⭢ηᶠ M') (hw : w ∉ M.fv) : w ∉ M'.fv := by
lemma step_not_fv (step : M ⭢ηᶠ M') : M.fv = M'.fv := by
induction step with
| base => grind
| abs =>
Expand Down
Loading