Theorems · Definition · order theory
BddBelow
{α : Type u_1} → [LE α] → Set α → PropA set is bounded below if there exists a lower bound.
- Defined in
- Mathlib.Order.Bounds.Defs
- Cited by
- 401 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 13 definitions · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Set.Nonemptyproof · cited by 2,627
- lowerBoundsproof · cited by 212
Cited by433
Results whose statement or proof uses this declaration.
- csInf_lestatement and proof · cited by 51
- OrderBot.bddBelowstatement · cited by 31
- ciInf_lestatement and proof · cited by 25
- isGLB_csInfstatement and proof · cited by 24
- BddBelow.monostatement · cited by 16
- csInf_le_csInfstatement and proof · cited by 9
- Bornology.IsBounded.bddBelowstatement · cited by 9
- DirectedOn.csInf_lestatement and proof · cited by 9
- csInf_of_not_bddBelowstatement and proof · cited by 8
- IsCompact.bddBelowstatement · cited by 8
- bddBelow_Iccstatement and proof · cited by 8
- DirectedOn.isGLB_csInfstatement and proof · cited by 8
Showing the 200 most cited of 433.