Proposition free_abmonoid_mor_eq {X : hSet} {Y : abmonoid} {f g : monoidfun (free_abmonoid X) Y} (p : ∏ (x : X), f (free_abmonoid_unit x) = g (free_abmonoid_unit x)) : f = g. Proof. use (invmaponpathsweq (invweq (free_abmonoid_universal_property X Y)) f g). use funextsec. exact p. Qed.
Require Import UniMath.MoreFoundations.Subtypes. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Combinatorics.Lists.