reserve
  X,x,y,z for set,
  k,n,m for Nat ,
  f for Function,
  p,q,r for FinSequence of NAT;
reserve p1,p2,p3 for FinSequence;

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;
