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feat(LocallyNameless/Untyped): FullEta.steps_open_cong_l #705

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feat(LocallyNameless/Untyped): FullEta.steps_open_cong_l #705

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7 changes: 7 additions & 0 deletions Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/FullEta.lean
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Expand Up @@ -156,6 +156,13 @@ lemma steps_open_cong_r {s t t' : Term Var} (lc_s : LC s.abs) (lc_t : LC t) (ste
case refl => rfl
case head _ _ st _ ih => exact .trans (step_open_cong_r lc_s lc_t st) (ih (step_lc_r st))

theorem steps_open_cong_l {s s' t : Term Var} (xs : Finset Var)
(h : ∀ x ∉ xs, (s ^ fvar x) ↠ηᶠ (s' ^ fvar x)) (h_lc : LC t) :
(s ^ t) ↠ηᶠ (s' ^ t) := by
have ⟨x, _⟩ := fresh_exists <| free_union [fv] Var
rw [Term.subst_intro x _ s (by grind), Term.subst_intro x _ s' (by grind)]
exact steps_subst_cong_l _ _ _ (h x (by grind)) h_lc

/- Closing a sequence of η-reduction steps over a fresh variable preserves the steps. -/
open Relation in
lemma close_eta_steps (hx_M : x ∉ M.fv) (st_M : ReflGen FullEta (M ^ fvar x) N) :
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