fact: Definition PowerObject_property {a b : C} : ∏ f : C ⟦ b ⨉ a, Ω ⟧, ∃! g : C ⟦ a, PowerObject_on_ob b ⟧, f = (identity b) ⨱ g · PowerObject_inPred b := (pr2 (pr2 P)) a b.
imports: UniMath.Foundations.PartA UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.SubobjectClassifier UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.OppositeCategory.Core UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Adjunctions.Core