fact: Definition monad_dist_laws (a : T ∙ S ⟹ S ∙ T) := (((∏ x : C, η S (T x) · a x = #T (η S x)) × (∏ x : C, #S (η T x) · a x = η T (S x))) × (∏ x : C, a (T x) · #T (a x) · μ T (S x) = #S (μ T x) · a x)) × (∏ x : C, #S (a x) · a (S x) · #T (μ S x) = μ S (T x) · a x).
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.LModules