
theorem :: MATRIX_4:6
  for M1,M2 being Matrix of COMPLEX st len M1=len M2 & width M1=width M2
  & M1 = M1 + M2 holds M2 = 0_Cx(len M1,width M1)
proof
  let M1,M2 be Matrix of COMPLEX;
  assume that
A1: len M1=len M2 & width M1=width M2 and
A2: M1 = M1 + M2;
  0_Cx(len M1,width M1)=M1+M2+(-M1) by A2,MATRIX_4:2
    .=Field2COMPLEX ((COMPLEX2Field M2)+(COMPLEX2Field M1) -(COMPLEX2Field
  M1)) by A1,MATRIX_3:2
    .=M2 by A1,MATRIX_4:21;
  hence thesis;
end;
