proposition: Lemma sn_power_arrow_unique (t : ∑ (f: C ⟦c', sn_power_object⟧), ∏ i, f · sn_power_projection i = cone' i) : t = (sn_power_arrow ,, sn_power_arrow_commutes).
proof: Proof. apply subtypePairEquality. { intro. apply impred_isaprop. intro. apply homset_property. } apply BinProductArrowUnique. - refine (!_ @ pr2 t _). apply maponpaths. exact (maponpaths _ (homotinvweqweq _ _)). - apply ProductArrowUnique. intro i. refine (_ @ pr2 t _). refine (assoc' _ _ _ @ _). refine (maponpaths _ (!_)). exact (maponpaths _ (homotinvweqweq _ _)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorCategory UniMath.Combinatorics.StandardFiniteSets