reserve w, w1, w2 for Element of ExtREAL;
reserve c, c1, c2 for Complex;
reserve A, B, C, D for complex-membered set;
reserve F, G, H, I for ext-real-membered set;
reserve a, b, s, t, z for Complex;
reserve f, g, h, i, j for ExtReal;
reserve r for Real;
reserve e for set;

theorem Th65:
  A--B = {c1-c2: c1 in A & c2 in B}
proof
  thus A--B c= {c1-c2: c1 in A & c2 in B}
  proof
    let e be object;
    assume e in A--B;
    then consider c1,c2 such that
A1: e = c1+c2 and
A2: c1 in A and
A3: c2 in --B;
    e = c1- -c2 & -c2 in B by A1,A3,Th12;
    hence thesis by A2;
  end;
  let e be object;
  assume e in {c1-c2: c1 in A & c2 in B};
  then consider c1,c2 such that
A4: e = c1-c2 & c1 in A and
A5: c2 in B;
  -c2 in --B by A5;
  hence thesis by A4;
end;
