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refactor(LocallyNameless): simplify proof of FullBeta.step_lc_r #740

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Merged
chenson2018 merged 2 commits into from
Jul 25, 2026
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refactor(LocallyNameless): simplify proof of FullBeta.step_lc_r #740

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refactor(LocallyNameless): simplify proof of FullBeta.step_lc_r
lengyijun Jul 22, 2026
3cea411
inline proof
chenson2018 Jul 25, 2026
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5 changes: 1 addition & 4 deletions Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/FullBeta.lean
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Expand Up @@ -77,10 +77,7 @@ variable [HasFresh Var] [DecidableEq Var]

/-- The right side of a reduction is locally closed. -/
@[scoped grind →]
lemma step_lc_r (step : M ⭢βᶠ M') : LC M' := by
induction step
case abs => constructor; assumption
all_goals grind
lemma step_lc_r (step : M ⭢βᶠ M') : LC M' := Xi.step_lc_r (by grind) step

lemma steps_lc_or_rfl {M M' : Term Var} (redex : M ↠βᶠ M') : (LC M ∧ LC M') ∨ M = M' := by
grind
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