reserve x for set,
  D for non empty set,
  k,n,m,i,j,l for Nat,
  K for Field;

theorem Th7:
  for A,B being Matrix of REAL st len A=len B & width A=width B &
  len A>0 holds A + (B - B) = A
proof
  let A,B be Matrix of REAL;
  assume A1: len A=len B & width A=width B;
  assume len A>0;
  hence A=A+(0_Rmatrix(len B,width B)) by A1,MATRIXR1:36
    .=MXF2MXR (MXR2MXF A)+ MXF2MXR ((MXR2MXF B)+(-(MXR2MXF B))) by MATRIX_4:2
    .=A + (B - B) by MATRIX_4:def 1;
end;
