Theorems · Theorem · order theory
Finset.exists_inf_le
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeInf β] [inst_1 : OrderTop β] [WellFoundedLT β] (f : α → β),
∃ t, ∀ (a : α), t.inf f ≤ f a- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Bot.botproof · cited by 4,720
- Set.rangeproof · cited by 4,705
- IsEmptyproof · cited by 759
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- WellFoundedLTstatement and proof · cited by 491
- isEmpty_or_nonemptyproof · cited by 269
- Finset.infstatement and proof · cited by 219
- Set.range_nonemptyproof · cited by 84
- isEmptyElimproof · cited by 59
- WellFounded.has_minproof · cited by 26
Cited by3
Results whose statement or proof uses this declaration.
- IsArtinianRing.setOfPred_isMaximal_finiteproof · cited by 2
- IsArtinian.isSemisimpleModule_iff_jacobsonproof · cited by 1
- Finset.exists_inf_eq_iInfproof · cited by 0