reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;

theorem Th26:
  x <> y implies <*x,y*> -| y = <*x*>
proof
  assume x <> y;
  then y..<*x,y*> = 1+1 by Th20;
  then
A1: 1 = y..<*x,y*>-1;
  rng<*x,y*> = { x,y } by Lm1;
  then y in rng<*x,y*> by TARSKI:def 2;
  hence <*x,y*> -| y = <*x,y*>| Seg 1 by A1,FINSEQ_4:33
    .= <*x*> by Th3;
end;
