•Let t = 8 x. t(x) ) 9 z.s(x, z)
•Assume wlog that t asserts xi ¹ xj forall i ¹ j. Denote ¹(x) the formula
Æi < j xi ¹ xj
–Hence t(x) = ¹(x) Æ t’(x)
•Similarly, s asserts z ¹ xi forall i.
Denote ¹(x, z) = Æi xi ¹ z
–Hence s(x, z) = t(x) Æ ¹(x, z) Æ s’(x, z)
where all
atomic predicates in s’(x, z) contain z
•Hence:
t = 8 x.(¹(x) Æ t’(x) ) 9 z. ¹(x,z) Æ s’(x, z))
•