fact: Definition isBinDirectSum (a b co : A) (i1 : a --> co) (i2 : b --> co) (p1 : co --> a) (p2 : co --> b) : hProp := i1 · p1 = 1 ∧ i2 · p2 = 1 ∧ i1 · p2 = 0 ∧ i2 · p1 = 0 ∧ p1 · i1 + p2 · i2 = 1.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.Algebra.BinaryOperations UniMath.Algebra.Groups UniMath.Algebra.Monoids UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis