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 Th155:
  r--F c= r--G implies F c= G
proof
  assume
A1: r--F c= r--G;
  let i;
  assume i in F;
  then r-i in r--F by Th152;
  then ex w st r-i = r-w & w in G by A1,Th154;
  hence thesis by XXREAL_3:12;
end;
