let i be Nat; :: thesis: for c1, c2 being Complex holds c1 * (i |-> c2) = i |-> (c1 * c2)
let c1, c2 be Complex; :: thesis: c1 * (i |-> c2) = i |-> (c1 * c2)
reconsider s1 = c1, s2 = c2 as Element of COMPLEX by XCMPLX_0:def 2;
s1 * (i |-> s2) = i |-> ((multcomplex [;] (s1,(id COMPLEX))) . s2) by FINSEQOP:16
.= i |-> (c1 * c2) by Lm1 ;
hence c1 * (i |-> c2) = i |-> (c1 * c2) ; :: thesis: verum