Theorems · Theorem · order theory

Finset.sup_induction

∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeSup α] [inst_1 : OrderBot α] {s : Finset β} {f : β → α}
  {p : α → Prop}, p ⊥ → (∀ (a₁ : α), p a₁ → ∀ (a₂ : α), p a₂ → p (a₁ ⊔ a₂)) → (∀ b ∈ s, p (f b)) → p (s.sup f)

Defined in

Mathlib.Data.Finset.Lattice.Fold

Cited by

8 results in Mathlib

Foundations

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

Assumes

SemilatticeSupOrderBot