s:QOSet, a, b, c:|s|. (a <s b)  (b <s c)  (a <s c) 

latex

Up	sets 1
Definitions of Statement	DSet, QOSet
Definitions	x,y. t(x;y), t  T, x:A. B(x), P & Q, DSet, x(s1,s2), P  Q, P  Q, P  Q, QOSet, Trans(T;x,y.E(x;y))
Lemmas	qoset wf, set lt is sp of leq, set leq wf, strict part wf, set lt wf, set car wf, trans functionality wrt iff, set leq trans, trans imp sp trans