let z1, z2 be Element of F_Complex ; :: thesis: ( z1 <> 0. F_Complex & z2 <> 0. F_Complex implies (z1 " ) / z2 = (z1 * z2) " )
reconsider z1' = z1, z2' = z2 as Element of COMPLEX by Def1;
assume A1: z1 <> 0. F_Complex ; :: thesis: ( not z2 <> 0. F_Complex or (z1 " ) / z2 = (z1 * z2) " )
assume A2: z2 <> 0. F_Complex ; :: thesis: (z1 " ) / z2 = (z1 * z2) "
then A3: z1 * z2 <> 0. F_Complex by A1, VECTSP_1:44;
z1 " = z1' " by A1, Th7;
hence (z1 " ) / z2 = (z1' " ) / z2' by A2, Th8
.= (z1' * z2') " by XCMPLX_1:223
.= (z1 * z2) " by A3, Th7 ;
:: thesis: verum