proposition: Lemma scalar_extension_preserves_monoid_monoid_action_is_monoid_action_morphism : ∏ x m, mor_action_ax scalar_extension_preserves_monoid_monoid_action_mor x m.
proof: Proof. intros x m. use (issurjsetquotpr _ x (_ ,, setproperty _ _ _) _). intro y. refine (!_ @ maponpaths (λ x, _ x * _) (pr2 y)). refine (!_ @ maponpaths (λ x, _ (_ x)) (pr2 y)). apply (!assocax _ _ _ _). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Algebra.Monoids UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total