Theorems · Theorem · order theory
Finset.le_inf_iff
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeInf α] [inst_1 : OrderTop α] {s : Finset β} {f : β → α} {a : α},
a ≤ s.inf f ↔ ∀ b ∈ s, a ≤ f b- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 54 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.
Cites7
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.valproof · cited by 438
- Finset.infstatement · cited by 219
- Multiset.mem_mapproof · cited by 72
- Multiset.le_infproof · cited by 3
Cited by12
Results whose statement or proof uses this declaration.
- Finset.inf_leproof · cited by 23
- Finset.le_infproof · cited by 10
- Finset.le_inf'_iffproof · cited by 10
- Finset.inf_product_leftproof · cited by 2
- Finset.inf_unionproof · cited by 1
- Finset.isGLB_infproof · cited by 1
- Finset.inf_commproof · cited by 1
- Finset.inf_constproof · cited by 1
- Finset.le_min_iffproof · cited by 0
- Finset.inf_prodMapproof · cited by 0
- Finset.inf_erase_topproof · cited by 0