Theorems · Theorem · order theory
Order.isGLB_Ioi_iff_isPredPrelimit
∀ {α : Type u_1} {a : α} [inst : LinearOrder α], IsGLB (Set.Ioi a) a ↔ Order.IsPredPrelimit a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.Ioistatement and proof · cited by 1,463
- Set.Iciproof · cited by 1,070
- CovByproof · cited by 290
- IsGLBstatement and proof · cited by 213
- Order.IsPredPrelimitstatement · cited by 93
- LT.lt.falseproof · cited by 66
- CovBy.ltproof · cited by 51
- IsGLB.uniqueproof · cited by 13
- isGLB_Iciproof · cited by 3
- CovBy.Ioi_eqproof · cited by 3
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