proposition: Lemma abgr_monic_kernel_in_hfiber_mult_eq {A B : abgr} (f : abgr_category⟦A, B⟧) (w : abgr) (x x' : w) (h : abgr_category⟦w, B⟧) (X : hfiber (pr1 f) (pr1 h x)) (X0 : hfiber (pr1 f) (pr1 h x')) : pr1 f (pr1 X * pr1 X0)%multmonoid = pr1 h (x * x')%multmonoid.
proof: Proof. rewrite (pr1 (pr2 f)). rewrite (pr2 X). rewrite (pr2 X0). rewrite (pr1 (pr2 h)). use idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.Algebra.BinaryOperations UniMath.Algebra.Groups UniMath.Algebra.Monoids UniMath.NumberSystems.Integers UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Abelian UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.BinDirectSums