theorem
  R1 c= P1 & R2 c= P2 implies R1 before R2 c= P1 before P2
proof
  assume that
A1: R1 c= P1 and
A2: R2 c= P2;
  let x be object;
  assume x in R1 before R2;
  then ex C1,C2 st ( x = C1^C2)&( C1 in R1)&( C2 in R2);
  hence thesis by A1,A2;
end;
