Theorems · Theorem · order theory

Finset.inf_le_iff

∀ {α : Type u_2} {ι : Type u_5} [inst : LinearOrder α] [inst_1 : OrderTop α] {s : Finset ι} {f : ι → α} {a : α},
  a < ⊤ → (s.inf f ≤ a ↔ ∃ b ∈ s, f b ≤ a)

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

LinearOrderOrderTop