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

theorem
  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 that
A1: len A=len B & width A=width B and
A2: len A>0;
  thus A + B - B =A + B+ - B by MATRIX_4:def 1
    .= A + (B +- B) by A1,MATRIX_3:3
    .= A+(B-B) by MATRIX_4:def 1
    .=A by A1,A2,Th7;
end;
