theorem
  <%>E in A & m > n implies A |^ n c= A |^ m
proof
  assume that
A1: <%>E in A and
A2: m > n;
  consider k such that
A3: n + k = m by A2,NAT_1:10;
  <%>E in A |^ k by A1,Th30;
  then A |^ n c= A |^ k ^^ A |^ n by Th16;
  hence thesis by A3,Th33;
end;
