(* Properties with sort-irrelevant equivalence for closures *****************)
-lemma fdeq_cpx_trans: ∀h,G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ≛ ⦃G2, L2, T⦄ →
- ∀T2. ⦃G2, L2⦄ ⊢ T ⬈[h] T2 →
- ∃∃T0. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T0 & ⦃G1, L1, T0⦄ ≛ ⦃G2, L2, T2⦄.
+lemma fdeq_cpx_trans: ∀h,G1,G2,L1,L2,T1,T. ⦃G1,L1,T1⦄ ≛ ⦃G2,L2,T⦄ →
+ ∀T2. ⦃G2,L2⦄ ⊢ T ⬈[h] T2 →
+ ∃∃T0. ⦃G1,L1⦄ ⊢ T1 ⬈[h] T0 & ⦃G1,L1,T0⦄ ≛ ⦃G2,L2,T2⦄.
#h #G1 #G2 #L1 #L2 #T1 #T #H #T2 #HT2
elim (fdeq_inv_gen_dx … H) -H #H #HL12 #HT1 destruct
elim (rdeq_cpx_trans … HL12 … HT2) #T0 #HT0 #HT02