let z1, z2 be Element of F_Complex ; :: thesis: ( z1 <> 0. F_Complex & z2 <> 0. F_Complex implies (z1 " ) / (z2 " ) = z2 / z1 )
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 " ) = z2 / z1 )
assume A2: z2 <> 0. F_Complex ; :: thesis: (z1 " ) / (z2 " ) = z2 / z1
A3: z1 " = z1' " by A1, Th7;
A4: z2 " = z2' " by A2, Th7;
z2 " <> 0. F_Complex by A2, VECTSP_1:74;
hence (z1 " ) / (z2 " ) = (z1' " ) / (z2' " ) by A3, A4, Th8
.= z2' / z1' by XCMPLX_1:216
.= z2 / z1 by A1, Th8 ;
:: thesis: verum