Theorems · Theorem · order theory
notMem_of_lt_csInf
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {x : α} {s : Set α}, x < sInf s → BddBelow s → x ∉ s- Cited by
- 5 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 935
- LT.lt.trans_leproof · cited by 678
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- lt_irreflproof · cited by 190
- csInf_leproof · cited by 51
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.exists_mul_lt_apply_of_lt_opNNNormproof · cited by 2
- notMem_of_lt_csInf'proof · cited by 2
- Besicovitch.TauPackage.color_ltproof · cited by 1
- ENNReal.essSup_restrict_eq_of_support_subsetproof · cited by 1
- ArchimedeanClass.stdPart_eq_sInfproof · cited by 1