proposition: Proposition dfl_eq_subst_equalizer_tm {Γ Δ : C} (s : Δ --> Γ) {A : ty Γ} (t₁ t₂ : comp_cat_tm Γ A) (p₁ p₂ : comp_cat_tm Δ (dfl_ext_identity_type t₁ t₂ [[ s ]])) : p₁ = p₂.
proof: Proof. use (invmaponpathsweq (invweq (dfl_full_comp_cat_tm_weq_mor _))) ; cbn. use (EqualizerArrowisMonic (preserves_equalizer_equalizer (pr2 (fiberwise_equalizers_dfl_full_comp_cat C) _ _ s) (dfl_ext_identity t₁ t₂))). apply (TerminalArrowEq (T := preserves_terminal_to_terminal _ (pr2 (fiberwise_terminal_dfl_full_comp_cat C) _ _ s) (dfl_full_comp_cat_terminal _))). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.FiberwiseTerminal UniMath.CategoryTheory.DisplayedCats.FiberwiseProducts UniMath.CategoryTheory.DisplayedCats.FiberwiseEqualizers UniMath.CategoryTheory.DisplayedCats.DependentSums UniMath.CategoryTheory.DisplayedCats.Codomain UniMath.CategoryTheory.DisplayedCats.FullyFaithfulDispFunctor UniMath.CategoryTheory.Monics UniMath.Bicategories.Core.Bicat UniMath.Bicategories.ComprehensionCat.BicatOfCompCat UniMath.Bicategories.ComprehensionCat.CompCatNotations UniMath.Bicategories.ComprehensionCat.DFLCompCat