feat(LocallyNameless/Untyped): generalize eta_subst_fvar#667
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`step_subst_cong_l` is the more general version
lengyijun
changed the title
eta_subst_fvar to eta_substeta_subst_fvar
chenson2018
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Jun 20, 2026
| induction steps with | ||
| | refl => rfl | ||
| | tail _ step ih => grind [step_subst_cong_l] | ||
| exact .single (Xi.abs {x} (by grind [step_subst_cong_l])) |
Collaborator
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It appears that (at the bottom of Properties) that we are missing a version of close_open_to_subst specialized to first openings, i.e. (m ^* x) ^ n = m [x := n] that if annotated with grind = would make the proof generated here better. Could you add this, please?
| s [ x := N ] ⭢ηᶠ s' [ x := N ] := by | ||
| induction step | ||
| case base h => cases h with | eta lc => exact Xi.base (.eta (subst_lc lc lc_N)) | ||
| case abs => grind [Xi.abs <| free_union Var, subst_open_var] |
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Probably better for performance:
Suggested change
| case abs => grind [Xi.abs <| free_union Var, subst_open_var] | |
| case abs => apply Xi.abs <| free_union Var; grind |
| /-- Abstracting then closing preserves a single η-reduction step. -/ | ||
| lemma step_abs_close {x} (step : M ⭢ηᶠ M') (lc_M : LC M) : (M ^* x).abs ⭢ηᶠ (M' ^* x).abs := by | ||
| grind [Xi.abs ∅] | ||
| grind [step_subst_cong_l, Xi.abs ∅] |
Collaborator
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Similarly here
Suggested change
| grind [step_subst_cong_l, Xi.abs ∅] | |
| apply Xi.abs ∅ | |
| grind [step_subst_cong_l] |
chenson2018
changed the title
eta_subst_fvareta_subst_fvar
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step_subst_cong_lis the more general version