theorem
  for P,A,B st 0 < P.B holds (P.A + P.B - 1)/ P.B <= P.|.B.A
proof
  let P,A,B such that
A1: 0 < P.B;
  (P.A + P.B - 1)/P.B <= P.(A /\ B)/P.B by A1,Th15,XREAL_1:72;
  hence thesis by A1,Def6;
end;
