reserve i,j for Nat;

theorem
  for A,B being Matrix of REAL st len A=len B & width A=width B & A+B=
  0_Rmatrix(len A,width A) holds B=-A
proof
  let A,B be Matrix of REAL;
  assume that
A1: len A=len B & width A=width B and
A2: A + B = 0_Rmatrix(len A,width A);
A3: len -MXR2MXF B=len MXR2MXF B & width -MXR2MXF B=width MXR2MXF B by
MATRIX_3:def 2;
  MXR2MXF(0_Rmatrix(len A,width A)) = (MXR2MXF A)+--(MXR2MXF B) by A2,
MATRIX_4:1
    .= (MXR2MXF A)-(-(MXR2MXF B)) by MATRIX_4:def 1;
  then MXR2MXF A = -MXR2MXF B by A1,A3,MATRIX_4:7;
  hence thesis by MATRIX_4:1;
end;
