theorem Th34:
  A c= B implies P.A <= P.B
proof
  assume A c= B;
  then P.(B \ A) = P.B - P.A by Th33;
  then 0 <= P.B - P.A by Def8;
  then 0 + P.A <= P.B by XREAL_1:19;
  hence thesis;
end;
