fact: Record partial_WO_ord (WO1 WO2:partial_WO) : Prop := { pwo_S_incl: Included (pwo_S WO1) (pwo_S WO2); pwo_restriction: forall x y:T, In (pwo_S WO1) x -> In (pwo_S WO1) y -> (pwo_R WO1 x y <-> pwo_R WO2 x y); pwo_downward_closed: forall x y:T, In (pwo_S WO1) y -> In (pwo_S WO2) x -> pwo_R WO2 x y -> In (pwo_S WO1) x }.
imports: Relation_Definitions Relation_Definitions_Implicit Classical_Wf Description FunctionalExtensionality Classical ZornsLemma ProofIrrelevance EnsemblesSpec