Theorems · Definition · order theory
IsLeast
{α : Type u_1} → [LE α] → Set α → α → Propa is a least element of a set s; for a partial order, it is unique if exists.
- Defined in
- Mathlib.Order.Bounds.Defs
- Cited by
- 122 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 12 definitions · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- lowerBoundsproof · cited by 212
Cited by128
Results whose statement or proof uses this declaration.
- IsLUBproof · cited by 280
- IsLeast.isGLBstatement and proof · cited by 23
- IsCompact.exists_isMinOnproof · cited by 15
- IsLeast.csInf_eqstatement and proof · cited by 11
- IsCompact.exists_isLeaststatement · cited by 9
- IsCompact.bddBelowproof · cited by 8
- isLeast_Icistatement · cited by 7
- IsCompact.sInf_memproof · cited by 5
- ScottContinuousOn.monotoneproof · cited by 5
- isLeast_singletonstatement · cited by 5
- ChainCompletePartialOrder.IsAdmissible.base_isLeaststatement · cited by 4
- isLUB_congrproof · cited by 4