Theorems · Theorem · order theory
Finset.le_inf
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeInf α] [inst_1 : OrderTop α] {s : Finset β} {f : β → α} {a : α},
(∀ b ∈ s, a ≤ f b) → a ≤ s.inf fAlias of the reverse direction of Finset.le_inf_iff.
- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInfOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- Finset.infstatement · cited by 219
- Finset.le_inf_iffproof · cited by 12
Cited by10
Results whose statement or proof uses this declaration.
- Finset.inf_eq_iInfproof · cited by 19
- Finset.inf'_eq_infproof · cited by 12
- Polynomial.trinomial_natTrailingDegreeproof · cited by 3
- Finset.inf_monoproof · cited by 2
- Finset.le_minproof · cited by 1
- Finset.inf_mono_funproof · cited by 1
- Finset.le_inf_constproof · cited by 1
- Finset.inf_Iciproof · cited by 1
- Finset.mul_inf_le_inf_mul_of_nonnegproof · cited by 0
- Finset.exists_inf_eq_iInfproof · cited by 0