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feat(LocallyNameless/Untyped): add FullEta.steps_lc_l #734

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feat(LocallyNameless/Untyped): add FullEta.steps_lc_l #734

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4 changes: 4 additions & 0 deletions Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/FullEta.lean
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Expand Up @@ -45,13 +45,17 @@ lemma step_lc_r (step : M ⭢ηᶠ M') : LC M' := by
grind

/-- The left side of an η-reduction is locally closed. -/
@[scoped grind →]
lemma step_lc_l [HasFresh Var] (step : M ⭢ηᶠ M') : LC M := by
induction step with
| base h_e => cases h_e with | eta => apply LC.abs ∅; grind
| appL lc_Z _ ih => exact LC.app lc_Z ih
| appR lc_Z _ ih => exact LC.app ih lc_Z
| @abs M' _ xs _ ih => exact LC.abs xs M' ih

lemma steps_lc_l [HasFresh Var] (step : M ↠ηᶠ M') (h : LC M') : LC M := by
induction step with grind

/-- Left congruence rule for application in multiple reduction. -/
theorem redex_app_l_cong (redex : M ↠ηᶠ M') (lc_N : LC N) : app M N ↠ηᶠ app M' N := by
induction redex <;> grind
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