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

theorem Th2:
  <*x*> is_a_prefix_of <*y*> implies x = y
proof
  assume
A1: <*x*> is_a_prefix_of <*y*>;
 len <*x*> = 1 & len <*y*> = 1 by FINSEQ_1:40;
then A2: <*x*> = <*y*> by A1,CARD_2:102;
 <*x*>.1 = x;
 hence thesis by A2,FINSEQ_1:40;
end;
