Definition cntabl(U:Type)(C:Ensemble(Ensemble U)):=
exists f:nat->Ensemble U,forall c,C c->exists i:nat,f i=c.

Lemma cntabl_P0(U:Type)(C:Ensemble(Ensemble U)) :cntabl _ C-> exists g:forall c,C c->nat, (forall c c' c'',g c c'=g c c'') /\forall c cc c' cc',g c c'=g cc cc'->c=cc.