fact: Variable chain_sup: forall S: Ensemble T, chain S -> { x:T | (forall y:T, In S y -> R y x) /\ (forall z:T, (forall y:T, In S y -> R y z) -> R x z) }.
imports: Classical ClassicalChoice Relation_Definitions Relation_Definitions_Implicit Ensembles EnsemblesImplicit ProofIrrelevance InverseImage EnsemblesSpec Quotients