-lemma fqup_ind: ∀b,G1,L1,T1. ∀R:relation3 ….
- (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
- (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐[b] ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → R G2 L2 T2.
-#b #G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
+lemma fqup_ind: ∀b,G1,L1,T1. ∀Q:relation3 ….
+ (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+ (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐[b] ⦃G2, L2, T2⦄ → Q G L T → Q G2 L2 T2) →
+ ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2.
+#b #G1 #L1 #T1 #Q #IH1 #IH2 #G2 #L2 #T2 #H
-lemma fqup_ind_dx: ∀b,G2,L2,T2. ∀R:relation3 ….
- (∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → R G1 L1 T1) →
- (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊐[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐+[b] ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
- ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → R G1 L1 T1.
-#b #G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
+lemma fqup_ind_dx: ∀b,G2,L2,T2. ∀Q:relation3 ….
+ (∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → Q G1 L1 T1) →
+ (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊐[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G L T → Q G1 L1 T1) →
+ ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G1 L1 T1.
+#b #G2 #L2 #T2 #Q #IH1 #IH2 #G1 #L1 #T1 #H