diff --git a/Mathlib/CategoryTheory/Limits/VanKampen.lean b/Mathlib/CategoryTheory/Limits/VanKampen.lean index 2c47495e645aa1..a89f2cf53055ae 100644 --- a/Mathlib/CategoryTheory/Limits/VanKampen.lean +++ b/Mathlib/CategoryTheory/Limits/VanKampen.lean @@ -686,9 +686,10 @@ theorem isVanKampenColimit_extendCofan {n : ℕ} (f : Fin (n + 1) → C) · simp only [Fin.cases_zero, m₁] · simp only [← m₂, colimit.ι_desc_assoc, Discrete.functor_obj, Cofan.mk_pt, Cofan.mk_ι_app, Fin.cases_succ] - induction' j using Fin.inductionOn with j _ - · exact t₂' ⟨WalkingPair.left⟩ - · have t₁' := (t₁ (Cofan.mk _ (Sigma.ι fun (j : Fin n) ↦ F.obj ⟨j.succ⟩)) (Discrete.natTrans + induction j using Fin.inductionOn with + | zero => exact t₂' ⟨WalkingPair.left⟩ + | succ j _ => + have t₁' := (t₁ (Cofan.mk _ (Sigma.ι fun (j : Fin n) ↦ F.obj ⟨j.succ⟩)) (Discrete.natTrans fun i ↦ α.app _) (Sigma.desc (fun j ↦ α.app _ ≫ c₁.inj _)) ?_ (NatTrans.equifibered_of_discrete _)).mp ⟨coproductIsCoproduct _⟩ ⟨j⟩ rotate_left