Theorems · Theorem · category theory

DirectLimit.induction

∀ {ι : Type u_1} [inst : Preorder ι] {F : ι → Type u_4} {T : ⦃i j : ι⦄ → i ≤ j → Sort u_8}
  (f : (i j : ι) → (h : i ≤ j) → T h) [inst_1 : ⦃i j : ι⦄ → (h : i ≤ j) → FunLike (T h) (F i) (F j)]
  [inst_2 : DirectedSystem F fun x1 x2 x3 => ⇑(f x1 x2 x3)] [inst_3 : IsDirectedOrder ι] {C : DirectLimit F f → Prop},
  (∀ (i : ι) (x : F i), C ⟦⟨i, x⟩⟧) → ∀ (x : DirectLimit F f), C x

Defined in

Mathlib.Order.DirectedInverseSystem

Cited by

17 results in Mathlib

Foundations

Depth 11 from the axioms · uses no axioms

Assumes

PreorderFunLikeDirectedSystemIsDirectedOrder