Theorems · Theorem · order theory
Finset.inf_le
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeInf α] [inst_1 : OrderTop α] {s : Finset β} {f : β → α} {b : β},
b ∈ s → s.inf f ≤ f b- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 23 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.
Cites6
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
- le_rflproof · cited by 1,558
- 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 by23
Results whose statement or proof uses this declaration.
- Finset.inf_eq_iInfproof · cited by 19
- Finset.inf'_eq_infproof · cited by 12
- Ideal.IsPrime.inf_le'proof · cited by 6
- Finset.min_leproof · cited by 6
- IsDedekindDomain.exists_sup_span_eqproof · cited by 2
- Finset.inf_le_iffproof · cited by 2
- Finset.inf_monoproof · cited by 2
- Finset.lt_inf_iffproof · cited by 2
- Ideal.eq_inf_of_isPrime_infproof · cited by 1
- BoxIntegral.Prepartition.splitMany_le_splitproof · cited by 1
- AlgebraicGeometry.exists_lift_of_germInjective_auxproof · cited by 1
- Finset.isGLB_infproof · cited by 1