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Work on the refactoring proof

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Yiyun Liu 2025-03-03 15:50:08 -05:00
parent fe418c2a78
commit 3e8ad2c5bc
3 changed files with 127 additions and 145 deletions
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13
theories/structural.v
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@ -794,18 +794,17 @@ Proof.
Unshelve. all: exact 0.
Qed.
Lemma Var_Inv Γ (i : nat) B A :
Lemma Var_Inv Γ (i : nat) A :
Γ ⊢ VarPTm i ∈ A ->
lookup i Γ B ->
⊢ Γ /\ Γ ⊢ B ≲ A.
⊢ Γ /\ exists B, lookup i Γ B /\ Γ ⊢ B ≲ A.
Proof.
move E : (VarPTm i) => u hu.
move : i E.
elim : Γ u A / hu=>//=.
- move => i Γ A hΓ hi i0 [?]. subst.
repeat split => //=.
have ? : A = B by eauto using lookup_deter. subst.
have h : Γ ⊢ VarPTm i ∈ B by eauto using T_Var.
- move => i Γ A hΓ hi i0 [*]. subst.
split => //.
exists A. split => //.
have h : Γ ⊢ VarPTm i ∈ A by eauto using T_Var.
eapply regularity in h.
move : h => [i0]?.
apply : Su_Eq. apply E_Refl; eassumption.