Theorems · Theorem · order theory
csInf_of_not_bddBelow
∀ {α : Type u_1} [inst : ConditionallyCompleteLinearOrder α] {s : Set α}, ¬BddBelow s → sInf s = sInf ∅- Cited by
- 8 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- InfSet.sInfstatement · cited by 935
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLinearOrder.csInf_of_not_bddBelowproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- ciInf_of_not_bddBelowproof · cited by 1
- csInf_eq_csInf_of_forall_exists_leproof · cited by 1
- csInf_eq_univ_of_not_bddBelowproof · cited by 1
- NNReal.toReal_limsupproof · cited by 1
- ENNReal.toReal_essSupproof · cited by 1
- Real.sInf_univproof · cited by 1
- Real.sSup_negproof · cited by 1
- ENNReal.toReal_limsupproof · cited by 1