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+ |^ (m, n) c= A |^.. m
proof
  let x be object;
  assume x in A+ |^ (m, n);
  then consider k such that
A1: m <= k and
  k <= n and
A2: x in A+ |^ k by FLANG_2:19;
  A+ |^ k c= A |^.. k by Th87;
  then
A3: x in A |^.. k by A2;
  A |^.. k c= A |^.. m by A1,Th5;
  hence thesis by A3;
end;
