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 Th6:
  k <= m implies A |^ (m, n) c= A |^.. k
proof
  assume
A1: k <= m;
    let x be object;
    assume x in A |^ (m, n);
    then consider l such that
A2: m <= l and
    l <= n and
A3: x in A |^ l by FLANG_2:19;
    k <= l by A1,A2,XXREAL_0:2;
    hence x in A |^.. k by A3,Th2;
end;
