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perf: try fixing the Subtype.weaken proof #674

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perf: try fixing the Subtype.weaken proof #674

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20 changes: 14 additions & 6 deletions Cslib/Languages/LambdaCalculus/LocallyNameless/Fsub/Subtype.lean
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Expand Up @@ -67,15 +67,23 @@ lemma refl (wf_Γ : Γ.Wf) (wf_σ : σ.Wf Γ) : Sub Γ σ σ := by
/-- Weakening of subtypes. -/
lemma weaken (sub : Sub (Γ ++ Θ) σ σ') (wf : (Γ ++ Δ ++ Θ).Wf) : Sub (Γ ++ Δ ++ Θ) σ σ' := by
generalize eq : Γ ++ Θ = ΓΘ at sub
induction sub generalizing Γ
case all =>
induction sub generalizing Γ with
| trans_tvar => grind [Ty.Wf.weaken, <= sublist_dlookup]
| all _ _ _ ih ih₂ =>
subst eq
apply all (free_union [Context.dom] Var) (ih wf rfl)
grind
| top _ σ_wf =>
subst eq
apply all (free_union [Context.dom] Var) <;> grind
all_goals grind [Ty.Wf.weaken, <= sublist_dlookup]
exact .top wf (weaken σ_wf wf.to_ok)
| refl_tvar _ fvar_wf =>
subst eq
exact Sub.refl_tvar wf (weaken fvar_wf wf.to_ok)
| _ => grind

lemma weaken_head (sub : Sub Δ σ σ') (wf : (Γ ++ Δ).Wf) : Sub (Γ ++ Δ) σ σ' := by
have eq : Γ ++ Δ = [] ++ Γ ++ Δ := by grind
grind [weaken]
rw [← List.nil_append Γ]
exact weaken sub wf

lemma narrow_aux
(trans : ∀ Γ σ τ, Sub Γ σ δ → Sub Γ δ τ → Sub Γ σ τ)
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