-(* Note: to be named fsb_ind when fsb becomes a definition like csx, lfsx ***)
-lemma fsb_ind_alt: ∀h,o. ∀R: relation3 …. (
- ∀G1,L1,T1. ≥[h,o] 𝐒⦃G1, L1, T1⦄ → (
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2
- ) → R G1 L1 T1
- ) →
- ∀G,L,T. ≥[h, o] 𝐒⦃G, L, T⦄ → R G L T.
-#h #o #R #IH #G #L #T #H elim H -G -L -T
-/4 width=1 by fsb_intro/
+lemma fsb_ind (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
+ ) →
+ ∀G,L,T. ≥𝐒 ❪G,L,T❫ → Q G L T.
+#Q #IH #G #L #T #H elim H -G -L -T
+#G1 #L1 #T1 #H1 #IH1
+@IH -IH [ /4 width=1 by SN3_intro/ ] -H1 #G2 #L2 #T2 #H
+elim (fpbc_inv_gen sfull … H) -H #H12 #Hn12 /3 width=1 by/