proposition: Proposition hset_struct_pointwise (P : hset_cartesian_closed_struct_data) {X Y Z : hSet} {PX : P X} {PY : P Y} {PZ : P Z} (f : X × Z → Y) (Pf : mor_hset_struct P (hset_struct_prod P PX PZ) PY f) (z : Z) : mor_hset_struct P PX PY (λ x : X, f (x ,, z)).
proof: Proof. exact (hset_struct_comp P (hset_struct_pair P (hset_struct_id P PX) (hset_struct_const P PX PZ z)) Pf). Qed.
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