qed-.
(* Basic_1: was: pc3_gen_lift *)
-lemma cpcs_inv_lift: ∀G,L,K,c,l,k. ⬇[c, l, k] L ≡ K →
- â\88\80T1,U1. â¬\86[l, k] T1 â\89¡ U1 â\86\92 â\88\80T2,U2. â¬\86[l, k] T2 â\89¡ U2 →
+lemma cpcs_inv_lift: ∀G,L,K,b,l,k. ⬇[b, l, k] L ≘ K →
+ â\88\80T1,U1. â¬\86[l, k] T1 â\89\98 U1 â\86\92 â\88\80T2,U2. â¬\86[l, k] T2 â\89\98 U2 →
⦃G, L⦄ ⊢ U1 ⬌* U2 → ⦃G, K⦄ ⊢ T1 ⬌* T2.
-#G #L #K #c #l #k #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HU12
+#G #L #K #b #l #k #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HU12
elim (cpcs_inv_cprs … HU12) -HU12 #U #HU1 #HU2
elim (cprs_inv_lift1 … HU1 … HLK … HTU1) -U1 #T #HTU #HT1
elim (cprs_inv_lift1 … HU2 … HLK … HTU2) -L -U2 #X #HXU
qed-.
(* Basic_1: was: pc3_lift *)
-lemma cpcs_lift: ∀G,L,K,c,l,k. ⬇[c, l, k] L ≡ K →
- â\88\80T1,U1. â¬\86[l, k] T1 â\89¡ U1 â\86\92 â\88\80T2,U2. â¬\86[l, k] T2 â\89¡ U2 →
+lemma cpcs_lift: ∀G,L,K,b,l,k. ⬇[b, l, k] L ≘ K →
+ â\88\80T1,U1. â¬\86[l, k] T1 â\89\98 U1 â\86\92 â\88\80T2,U2. â¬\86[l, k] T2 â\89\98 U2 →
⦃G, K⦄ ⊢ T1 ⬌* T2 → ⦃G, L⦄ ⊢ U1 ⬌* U2.
-#G #L #K #c #l #k #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HT12
+#G #L #K #b #l #k #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HT12
elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
elim (lift_total T l k) /3 width=12 by cprs_div, cprs_lift/
qed.