Theorems · Theorem · order theory

disjointedRec

∀ {α : Type u_1} {ι : Type u_2} [inst : GeneralizedBooleanAlgebra α] [inst_1 : Preorder ι]
  [inst_2 : LocallyFiniteOrderBot ι] {f : ι → α} {p : α → Prop},
  (∀ ⦃t : α⦄ ⦃i : ι⦄, p t → p (t \ f i)) → ∀ ⦃i : ι⦄, p (f i) → p (disjointed f i)

An induction principle for disjointed. To prove something about disjointed f i, it's enough to prove it for f i and being able to extend through diffs.

Defined in

Mathlib.Order.Disjointed

Cited by

3 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GeneralizedBooleanAlgebraPreorderLocallyFiniteOrderBot