Theorems · Theorem · order theory
OrderBot.bddBelow
∀ {α : Type u_1} [inst : Preorder α] [OrderBot α] (s : Set α), BddBelow sWhen there is a global minimum, every set is bounded below.
- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by31
Results whose statement or proof uses this declaration.
- csInf_le'proof · cited by 9
- tendsto_atTop_iInfproof · cited by 6
- ciInf_le'proof · cited by 6
- NNReal.coe_sInfproof · cited by 5
- csInf_eq_bot_of_bot_memproof · cited by 4
- MeasureTheory.upperCrossingTime_lt_of_le_upcrossingsBeforeproof · cited by 3
- rieszContentAux_leproof · cited by 2
- ContinuousLinearMap.exists_mul_lt_apply_of_lt_opNNNormproof · cited by 2
- csInf_le_csInf'proof · cited by 2
- notMem_of_lt_csInf'proof · cited by 2
- NNReal.tendsto_agmSequences_snd_agmproof · cited by 2
- ENat.natCast_sInfproof · cited by 2