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
  A c= B & C c= D implies A///C c= B///D
proof
  assume
A1: A c= B & C c= D;
  let z;
A2: A///C = {c1/c2: c1 in A & c2 in C} by Th115;
  assume z in A///C;
  then ex c,c1 st z = c/c1 & c in A & c1 in C by A2;
  hence thesis by A1,Th116;
end;
