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

theorem Th50:
  p1 <> p2 implies <*p1,p2,p3*>-:p2 = <*p1,p2*>
proof
  assume
A1: p1 <> p2;
  rng<*p1,p2,p3*> = { p1,p2,p3 } by Lm2;
  then p2 in rng<*p1,p2,p3*> by ENUMSET1:def 1;
  hence <*p1,p2,p3*>-:p2 = (<*p1,p2,p3*> -| p2)^<*p2*> by Th40
    .= <*p1,p2*> by A1,Th27;
end;
