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 Th4:
  <*x*>,<*y*> are_c=-comparable implies x = y
proof
    assume
A1: <*x*>,<*y*> are_c=-comparable;
 len <*x*> = 1 & len <*y*> = 1 by FINSEQ_1:40;
then A2: <*x*> = <*y*> by A1,Th3;
    <*x*>.1 = x;
    hence thesis by A2,FINSEQ_1:40;
end;
