fact: Definition hset_struct_type_prod_laws {P : hset_struct} {I : UU} (HP : hset_struct_type_prod_data P I) : UU := (∏ (D : I → hSet) (PD : ∏ (i : I), P (D i)) (i : I), mor_hset_struct P (HP D PD) (PD i) (λ f, f i)) × (∏ (D : I → hSet) (PD : ∏ (i : I), P (D i)) (W : hSet) (PW : P W) (fs : ∏ (i : I), W → D i) (Pfs : ∏ (i : I), mor_hset_struct P PW (PD i) (fs i)), mor_hset_struct P PW (HP D PD) (λ w i, fs i w)).
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Binproducts UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.MonadAlgebras UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure