(* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
-(* Properties with degree-based equivalence on closures *********************)
+(* Properties with sort-irrelevant equivalence on closures ******************)
-lemma fdeq_lpxs_trans (h) (o): ∀G1,G2,L1,L0,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L0, T2⦄ →
- ∀L2. ⦃G2, L0⦄ ⊢⬈*[h] L2 →
- ∃∃L. ⦃G1, L1⦄ ⊢⬈*[h] L & ⦃G1, L, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G2 #L1 #L0 #T1 #T2 #H1 #L2 #HL02
+lemma fdeq_lpxs_trans (h): ∀G1,G2,L1,L0,T1,T2. ⦃G1, L1, T1⦄ ≛ ⦃G2, L0, T2⦄ →
+ ∀L2. ⦃G2, L0⦄ ⊢⬈*[h] L2 →
+ ∃∃L. ⦃G1, L1⦄ ⊢⬈*[h] L & ⦃G1, L, T1⦄ ≛ ⦃G2, L2, T2⦄.
+#h #G1 #G2 #L1 #L0 #T1 #T2 #H1 #L2 #HL02
elim (fdeq_inv_gen_dx … H1) -H1 #HG #HL10 #HT12 destruct
elim (rdeq_lpxs_trans … HL02 … HL10) -L0 #L0 #HL10 #HL02
/3 width=3 by fdeq_intro_dx, ex2_intro/