theorem Th49:
  p1 <> p2 implies <*p1,p2*>-:p2 = <*p1,p2*>
proof
  assume
A1: p1 <> p2;
  rng<*p1,p2*> = { p1,p2 } by Lm1;
  then p2 in rng<*p1,p2*> by TARSKI:def 2;
  hence <*p1,p2*>-:p2 = (<*p1,p2*> -| p2)^<*p2*> by Th40
    .= <*p1,p2*> by A1,Th26;
end;
