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This file axiomatizes the relational form of the axiom of choice
Axiom relational_choice :
  forall (A B : Type) (R : A->B->Prop),
   (forall x : A, exists y : B, R x y) ->
     exists R' : A->B->Prop,
       subrelation R' R /\ forall x : A, exists! y : B, R' x y.