reserve E, x, y, X for set;
reserve A, B, C, D for Subset of E^omega;
reserve a, a1, a2, b, c, c1, c2, d, ab, bc for Element of E^omega;
reserve e for Element of E;
reserve i, j, k, l, n, n1, n2, m for Nat;

theorem Th46:
  A c= C* & B c= C* implies A ^^ B c= C*
proof
  assume
A1: A c= C* & B c= C*;
  thus thesis
  proof
    let x be object;
    assume x in A ^^ B;
    then ex a, b st a in A & b in B & x = a ^ b by Def1;
    hence thesis by A1,Th45;
  end;
end;
