
theorem :: MATRIX_4:8
  for M1,M2 being Matrix of COMPLEX st len M1=len M2 & width M1=width M2
  & M1+M2= 0_Cx(len M1,width M1) holds M2=-M1
proof
  let M1,M2 be Matrix of COMPLEX;
  assume that
A1: len M1=len M2 & width M1=width M2 and
A2: M1 + M2 = 0_Cx(len M1,width M1);
A3: len -M2=len M2 & width -M2=width M2 by MATRIX_3:def 2;
  COMPLEX2Field(0_Cx(len M1,width M1)) = (COMPLEX2Field M1)-(-(
  COMPLEX2Field M2)) by A2,MATRIX_4:1;
  then COMPLEX2Field M1 = -COMPLEX2Field M2 by A1,A3,MATRIX_4:7;
  hence thesis by MATRIX_4:1;
end;
