for P1, P2 being RelStr st RelStr(# the carrier of P1, the InternalRel of P1 #) = RelStr(# the carrier of P2, the InternalRel of P2 #) holds
for X being set
for a1 being Element of P1
for a2 being Element of P2 st a1 = a2 holds
( ( X is_<=_than a1 implies X is_<=_than a2 ) & ( X is_>=_than a1 implies X is_>=_than a2 ) ) by Th1;