Theorems · Theorem · order theory

Finset.inf_induction

∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeInf α] [inst_1 : OrderTop 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.inf f)

Defined in

Mathlib.Data.Finset.Lattice.Fold

Cited by

2 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemilatticeInfOrderTop