fact: Record partial_injection : Type := { pi_dom: Ensemble X; pi_func: forall x:X, In pi_dom x -> Y; pi_inj: forall (x1 x2:X) (i1:In pi_dom x1) (i2:In pi_dom x2), pi_func x1 i1 = pi_func x2 i2 -> x1 = x2 }.
imports: FunctionProperties Relation_Definitions Relation_Definitions_Implicit CSB EnsemblesSpec ClassicalChoice ZornsLemma EnsemblesImplicit ProofIrrelevance FunctionalExtensionality Description