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feat: FullEta.steps_fv #807

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feat: FullEta.steps_fv #807

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4 changes: 3 additions & 1 deletion Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/FullEta.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -75,13 +75,15 @@ variable [HasFresh Var] [DecidableEq Var]
/-- An η-reduction step does not introduce new free variables. -/
lemma step_not_fv (step : M ⭢ηᶠ M') : M.fv = M'.fv := by
induction step with
| base => grind
| abs =>
have ⟨x, _⟩ := fresh_exists <| free_union [fv] Var
have := open_close x
grind [open_preserve_not_fvar]
| _ => grind

lemma steps_fv (steps : M ↠ηᶠ M') : M.fv = M'.fv := by
induction steps with grind [step_not_fv]

/- `s ⭢ηᶠ s'` implies `s[x := N] ⭢ηᶠ s'[x := N]`. -/
lemma step_subst_cong_l {x : Var} (s s' N : Term Var) (step : s ⭢ηᶠ s') (lc_N : LC N) :
s[x := N] ⭢ηᶠ s'[x := N] := by
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