Theorems · Theorem · commutative algebra

Ring.DirectLimit.induction_on

∀ {ι : Type u_1} [inst : Preorder ι] {G : ι → Type u_2} [inst_1 : (i : ι) → CommRing (G i)]
  {f : (i j : ι) → i ≤ j → G i → G j} [Nonempty ι] [IsDirectedOrder ι] {C : Ring.DirectLimit G f → Prop}
  (z : Ring.DirectLimit G f), (∀ (i : ι) (x : G i), C ((Ring.DirectLimit.of G f i) x)) → C z

Defined in

Mathlib.Algebra.Colimit.Ring

Cited by

2 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderCommRingNonemptyIsDirectedOrder