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Add more cases to the soundness proof

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Yiyun Liu 2025-02-12 20:18:12 -05:00
parent 48adb34946
commit ba77752329
2 changed files with 34 additions and 15 deletions
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16
theories/structural.v
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@ -658,3 +658,19 @@ Proof.
by asimpl.
by asimpl.
Qed.
Lemma Su_Sig_Proj2_Var n Γ (A0 A1 : PTm n) B0 B1 :
Γ ⊢ PBind PSig A0 B0 ≲ PBind PSig A1 B1 ->
funcomp (ren_PTm shift) (scons A0 Γ) ⊢ B0 ≲ B1.
Proof.
move => h.
have /Su_Sig_Proj1 h1 := h.
have /regularity_sub0 [i h2] := h1.
move /weakening_su : (h) h2. move => /[apply].
move => h2.
apply : Su_Sig_Proj2'; try eassumption; rewrite -?/ren_PTm; cycle 2.
apply E_Refl. apply T_Var' with (i := var_zero); eauto.
sfirstorder use:wff_mutual.
by asimpl.
by asimpl.
Qed.