let D be non empty set ; :: thesis: for d1, d2 being Element of D
for g being BinOp of D holds g "**" <*d1,d2*> = g . (d1,d2)
let d1, d2 be Element of D; :: thesis: for g being BinOp of D holds g "**" <*d1,d2*> = g . (d1,d2)
let g be BinOp of D; :: thesis: g "**" <*d1,d2*> = g . (d1,d2)
A1: len <*d1*> = 1 by FINSEQ_1:39;
thus g "**" <*d1,d2*> = g "**" (<*d1*> ^ <*d2*>) by FINSEQ_1:def 9
.= g . ((g "**" <*d1*>),d2) by A1, Th4
.= g . (d1,d2) by Lm4 ; :: thesis: verum