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 Th66:
  a in C+ & b in C+ implies a ^ b in C+
proof
  assume that
A1: a in C+ and
A2: b in C+;
  consider l such that
  l > 0 and
A3: b in C |^ l by A2,Th48;
  consider k such that
A4: k > 0 and
A5: a in C |^ k by A1,Th48;
  a ^ b in C |^ (k + l) by A5,A3,FLANG_1:40;
  hence thesis by A4,Th48;
end;
