∧∧ ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃V⦄ & ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃T⦄ & 𝐒⦃T⦄.
#h #G #L #V1 #T1 #HVT1 @and3_intro
[ #V2 #HV2 lapply (HVT1 (ⓐV2.T1) ?) -HVT1 /2 width=1 by cpx_pair_sn/ -HV2
- #H elim (tdeq_inv_pair … H) -H //
+ #H elim (teqx_inv_pair … H) -H //
| #T2 #HT2 lapply (HVT1 (ⓐV1.T2) ?) -HVT1 /2 width=1 by cpx_flat/ -HT2
- #H elim (tdeq_inv_pair … H) -H //
+ #H elim (teqx_inv_pair … H) -H //
| generalize in match HVT1; -HVT1 elim T1 -T1 * //
#p * #W1 #U1 #_ #_ #H
[ elim (lifts_total V1 (𝐔❴1❵)) #V2 #HV12
lapply (H (ⓓ{p}W1.ⓐV2.U1) ?) -H /2 width=3 by cpx_theta/ -HV12
- #H elim (tdeq_inv_pair … H) -H #H destruct
+ #H elim (teqx_inv_pair … H) -H #H destruct
| lapply (H (ⓓ{p}ⓝW1.V1.U1) ?) -H /2 width=1 by cpx_beta/
- #H elim (tdeq_inv_pair … H) -H #H destruct
+ #H elim (teqx_inv_pair … H) -H #H destruct
]
]
qed-.
⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃ⓐV.T⦄.
#h #G #L #V #T #HV #HT #HS #X #H elim (cpx_inv_appl1_simple … H) -H //
#V0 #T0 #HV0 #HT0 #H destruct
-@tdeq_pair [ @HV | @HT ] // (**) (* auto fails because δ-expansion gets in the way *)
+@teqx_pair [ @HV | @HT ] // (**) (* auto fails because δ-expansion gets in the way *)
qed.