lemma fsb_feqg_trans (S):
reflexive … S → symmetric … S → Transitive … S →
- â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9dªG1,L1,T1â\9d« →
- â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89\9b[S] â\9dªG2,L2,T2â\9d« â\86\92 â\89¥ð\9d\90\92 â\9dªG2,L2,T2â\9d«.
-#S #H1S #H2S #H3S #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
+ â\88\80G1,L1,T1. â\89¥ð\9d\90\92 â\9d¨G1,L1,T1â\9d© →
+ â\88\80G2,L2,T2. â\9d¨G1,L1,T1â\9d© â\89\9b[S] â\9d¨G2,L2,T2â\9d© â\86\92 â\89¥ð\9d\90\92 â\9d¨G2,L2,T2â\9d©.
+#S #H1S #H2S #H3S #G1 #L1 #T1 #H @(fsb_ind … H) -G1 -L1 -T1
#G1 #L1 #T1 #_ #IH #G2 #L2 #T2 #H12
@fsb_intro #G #L #T #H2
elim (feqg_fpbc_trans … H12 … H2) -G2 -L2 -T2