x in COMPLEX by XCMPLX_0:def 2;
then reconsider aa = x as Element of F_Complex by COMPLFLD:def 1;
let C1, C2 be Matrix of COMPLEX; :: thesis: ( ( for ea being Element of F_Complex st ea = x holds
C1 = Field2COMPLEX (ea * (COMPLEX2Field A)) ) & ( for ea being Element of F_Complex st ea = x holds
C2 = Field2COMPLEX (ea * (COMPLEX2Field A)) ) implies C1 = C2 )
assume that
A1: for ea being Element of F_Complex st ea = x holds
C1 = Field2COMPLEX (ea * (COMPLEX2Field A)) and
A2: for ea being Element of F_Complex st ea = x holds
C2 = Field2COMPLEX (ea * (COMPLEX2Field A)) ; :: thesis: C1 = C2
C2 = Field2COMPLEX (aa * (COMPLEX2Field A)) by A2;
hence C1 = C2 by A1; :: thesis: verum