proposition: Lemma lift_constant_eq (T : algebraic_theory) {n : nat} (f f' : T 0) (g : stn 0 → T n) (H : f = f') : lift_constant n f = f' • g.
proof: Proof. induction H. refine (maponpaths (comp f) _). apply funextfun. intro x. apply fromempty. exact (negnatlthn0 _ (stnlt x)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.coslicecat UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.Vectors UniMath.AlgebraicTheories.AlgebraCategory UniMath.AlgebraicTheories.AlgebraCategoryCore UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.AlgebraicTheoryCategoryCore UniMath.AlgebraicTheories.AlgebraicTheoryMorphisms UniMath.AlgebraicTheories.AlgebraMorphisms UniMath.AlgebraicTheories.Algebras