let i be Nat; :: thesis: for c1, c2 being Complex holds mlt ((i |-> c1),(i |-> c2)) = i |-> (c1 * c2)
let c1, c2 be Complex; :: thesis: mlt ((i |-> c1),(i |-> c2)) = i |-> (c1 * c2)
reconsider s1 = c1, s2 = c2 as Element of COMPLEX by XCMPLX_0:def 2;
mlt ((i |-> s1),(i |-> s2)) = s1 * (i |-> s2) by Th27
.= i |-> (c1 * c2) by Th22 ;
hence mlt ((i |-> c1),(i |-> c2)) = i |-> (c1 * c2) ; :: thesis: verum