let K be non empty multMagma ; for a1, a2, b1, b2 being Element of K holds mlt <*a1,a2*>,<*b1,b2*> = <*(a1 * b1),(a2 * b2)*>
let a1, a2, b1, b2 be Element of K; mlt <*a1,a2*>,<*b1,b2*> = <*(a1 * b1),(a2 * b2)*>
( <*a1,a2*> = <*a1*> ^ <*a2*> & <*b1,b2*> = <*b1*> ^ <*b2*> )
by FINSEQ_1:def 9;
hence mlt <*a1,a2*>,<*b1,b2*> =
(mlt <*a1*>,<*b1*>) ^ <*(a2 * b2)*>
by FINSEQOP:11
.=
<*(a1 * b1)*> ^ <*(a2 * b2)*>
by FINSEQ_2:88
.=
<*(a1 * b1),(a2 * b2)*>
by FINSEQ_1:def 9
;
verum