theorem Th5:
  for p,q being finite set st p c< q holds card p < card q
proof
  let p,q be finite set;
  assume that
A1: p c= q and
A2: p <> q;
A3: card p <= card q by A1,NAT_1:43;
  p,q are_c=-comparable by A1;
  hence thesis by A3,A2,Th3,XXREAL_0:1;
end;
