
theorem
  for M being Matrix of COMPLEX holds M+M = 2*M
proof
  reconsider e2=(1_F_Complex) + (1_F_Complex) as Element of F_Complex;
  let M be Matrix of COMPLEX;
A1: (1_F_Complex)*(COMPLEX2Field M)= COMPLEX2Field M by Th9;
  2 * M = Field2COMPLEX (e2*(COMPLEX2Field M)) by Def7,COMPLEX1:def 4
,COMPLFLD:8
    .=Field2COMPLEX ((COMPLEX2Field M)+(COMPLEX2Field M)) by A1,Th12;
  hence thesis;
end;
