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Set Universe Polymorphism.
Notation paths := identity .
Definition UU := Set.
Definition dirprod ( X Y : UU ) := sigT ( fun x : X => Y ) .
Definition dirprodpair { X Y : UU } := existT ( fun x : X => Y ) .
Definition hProp := sigT (fun X : Type => admit).
Definition hProptoType := @projT1 _ _ : hProp -> Type .
Coercion hProptoType: hProp >-> Sortclass.
Definition UU' := Type.
Definition hSet:= sigT (fun X : UU' => admit) .
Definition pr1hSet:= @projT1 UU (fun X : UU' => admit) : hSet -> Type.
Coercion pr1hSet: hSet >-> Sortclass.
Definition hrel ( X : UU ) := X -> X -> hProp.
Definition setquot { X : UU } ( R : hrel X ) : Type := sigT (fun A => iseqclass R A).
Definition iscomprelfun2 { X Y : UU } ( R : hrel X ) ( f : X -> X -> Y )
:= forall x x' x0 x0' : X , R x x' ->  R x0 x0' ->  paths ( f x x0 ) ( f x' x0' ) .

Axiom setquotuniv : forall  { X : UU } ( R : hrel X ) ( Y : hSet ) ( f : X -> Y ) ( c : setquot R ), Y .