reserve E, x, y, X for set;
reserve A, B, C for Subset of E^omega;
reserve a, a1, a2, b for Element of E^omega;
reserve i, k, l, m, n for Nat;

theorem
  A c= C+ & B c= C+ implies A ^^ B c= C+
proof
  assume that
A1: A c= C+ and
A2: B c= C+;
    let x be object;
    assume x in A ^^ B;
    then ex a, b st a in A & b in B & x = a ^ b by FLANG_1:def 1;
    hence x in C+ by A1,A2,Th66;
end;
