proposition: Proposition double_hor_comp_mor_transportf_disp_mor2_right_idpath {C : category} {D : twosided_disp_cat C C} (Cm : hor_comp D) {x₁ x₂ y₁ y₂ z₁ z₂ : C} {v₁ : x₁ --> x₂} {v₂ v₂' : y₁ --> y₂} (q : v₂ = v₂') {v₃ v₃' : z₁ --> z₂} (r : v₃ = v₃') {h₁ : D x₁ y₁} {h₂ : D y₁ z₁} {k₁ : D x₂ y₂} {k₂ : D y₂ z₂} (s₁ : h₁ -->[ v₁ ][ v₂' ] k₁) (s₂ : h₂ -->[ v₂ ][ v₃ ] k₂) : double_hor_comp_mor Cm s₁ (transportf_disp_mor2 q r s₂) = transportf_disp_mor2 (idpath _) r (double_hor_comp_mor Cm (transportf_disp_mor2 (idpath _) (!q) s₁) s₂).
proof: Proof. induction q, r ; cbn. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos