proposition: Lemma algebraic_theory_morphism_eq {T T' : algebraic_theory} (F F' : algebraic_theory_morphism T T') (H1 : ∏ n f, F n f = F' n f) : F = F'.
proof: Proof. use subtypePath. { intro. exact isapropunit. } use subtypePath. { intro. apply isapropdirprod; repeat (apply impred_isaprop; intro); apply setproperty. } do 2 (apply funextsec; intro). apply H1. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.Combinatorics.StandardFiniteSets UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.AlgebraicTheoryCategoryCore UniMath.AlgebraicTheories.IndexedSetCategory