Theorems · Theorem · order theory
UpperSet.infIrred_iff_of_finite
∀ {α : Type u_1} [inst : PartialOrder α] {s : UpperSet α} [Finite α], InfIrred s ↔ ∃ a, UpperSet.Ici a = s- Defined in
- Mathlib.Order.Birkhoff
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- PartialOrderstatement and proof · cited by 6,410
- Finitestatement and proof · cited by 3,029
- LT.lt.ne'proof · cited by 1,417
- UpperSetstatement and proof · cited by 245
- Set.toFiniteproof · cited by 174
- Minimalproof · cited by 150
- UpperSet.Icistatement and proof · cited by 38
- InfIrredstatement and proof · cited by 27
- UpperSet.eraseproof · cited by 9
- UpperSet.infIrred_Iciproof · cited by 4
- UpperSet.erase_inf_Iciproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- OrderIso.infIrredUpperSet_symm_applyproof · cited by 0