
theorem Th1:
  for P1,P2 being RelStr st the RelStr of P1 = the RelStr of P2 for
  a1,b1 being Element of P1 for a2,b2 being Element of P2 st a1 = a2 & b1 = b2
  holds (a1 <= b1 implies a2 <= b2) & (a1 < b1 implies a2 < b2)
proof
  let P1,P2 be RelStr such that
A1: the RelStr of P1 = the RelStr of P2;
  let a1,b1 be Element of P1;
  let a2,b2 be Element of P2;
A2: a2 <= b2 iff [a2,b2] in the InternalRel of P2;
  a1 <= b1 iff [a1,b1] in the InternalRel of P1;
  hence thesis by A1,A2;
end;
