theorem
  P1 c= P2 & Y1 c= Y2 implies Y1|`P1 c= Y2|`P2
proof
  assume P1 c= P2 & Y1 c= Y2;
  then Y1|`P1 c= Y1|`P2 & Y1|`P2 c= Y2|`P2 by Th94,Th95;
  hence thesis;
end;
