-lemma fsb_ind_fpbg_fpbs: ∀h. ∀Q:relation3 genv lenv term.
- (∀G1,L1,T1. ≥[h] 𝐒⦃G1, L1, T1⦄ →
- (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
- Q G1 L1 T1
- ) →
- ∀G1,L1,T1. ≥[h] 𝐒⦃G1, L1, T1⦄ →
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄ → Q G2 L2 T2.
-#h #Q #IH1 #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
+lemma fsb_ind_fpbg_fpbs (Q:relation3 …):
+ (∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
+ (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → Q G2 L2 T2) →
+ Q G1 L1 T1
+ ) →
+ ∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
+ ∀G2,L2,T2. ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ → Q G2 L2 T2.
+#Q #IH1 #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1