let A, B be complex-membered set ; :: thesis: for a, b being complex number st a in A & b in B holds
a / b in A /// B
let a, b be complex number ; :: thesis: ( a in A & b in B implies a / b in A /// B )
A1: A /// B = { (c1 / c2) where c1, c2 is Element of COMPLEX : ( c1 in A & c2 in B ) } by Th121;
( a in COMPLEX & b in COMPLEX ) by XCMPLX_0:def 2;
hence ( a in A & b in B implies a / b in A /// B ) by A1; :: thesis: verum