proposition: Proposition closed_under_fun_lam {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) : mor_hset_struct P PZ (hset_struct_fun P PX PY) (λ z, _ ,, hset_struct_pointwise P f Pf z).
proof: Proof. exact (pr22 P X Y Z PX PY PZ f 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