let D be non empty set ; :: thesis: for d1, d2, d3 being Element of D
for g being BinOp of D holds g "**" <*d1,d2,d3*> = g . (g . d1,d2),d3
let d1, d2, d3 be Element of D; :: thesis: for g being BinOp of D holds g "**" <*d1,d2,d3*> = g . (g . d1,d2),d3
let g be BinOp of D; :: thesis: g "**" <*d1,d2,d3*> = g . (g . d1,d2),d3
A1: len <*d1,d2*> = 2 by FINSEQ_1:61;
thus g "**" <*d1,d2,d3*> = g "**" (<*d1,d2*> ^ <*d3*>) by FINSEQ_1:60
.= g . (g "**" <*d1,d2*>),d3 by A1, Th5
.= g . (g . d1,d2),d3 by Th13 ; :: thesis: verum