reserve i,j for Nat;

theorem Th25:
  for A,B being Matrix of REAL holds len (A+B) = len A & width (A+
B)=width A & for i,j holds [i,j] in Indices A implies (A+B)*(i,j) = A*(i,j) + B
  *(i,j)
proof
  let A,B be Matrix of REAL;
  thus len (A+B) = len A & width (A+B)=width A by MATRIX_3:def 3;
  let i,j;
  assume [i,j] in Indices A;
  then (A+B)*(i,j)=(MXR2MXF A)*(i,j) + (MXR2MXF B)*(i,j) by MATRIX_3:def 3;
  hence thesis;
end;
