Theorems · Theorem · order theory
IsGLB.csInf_eq
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α} {a : α}, IsGLB s a → s.Nonempty → sInf s = a- Cited by
- 13 results in Mathlib
- Foundations
- Depth 10 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
- Set.Nonemptystatement and proof · cited by 2,627
- InfSet.sInfstatement · cited by 935
- ConditionallyCompleteLatticestatement and proof · cited by 364
- IsGLBstatement and proof · cited by 213
- isGLB_csInfproof · cited by 24
- IsGLB.uniqueproof · cited by 13
Cited by13
Results whose statement or proof uses this declaration.
- csInf_image2_eq_csInf_csInfproof · cited by 5
- csInf_Iooproof · cited by 4
- IsGLB.mem_of_nonempty_of_not_isPredLimitproof · cited by 2
- Seminorm.gauge_ballproof · cited by 2
- MonotoneOn.sInf_image_Iccproof · cited by 1
- RightOrdContinuous.map_csInfproof · cited by 1
- SimpleGraph.turanDensity_eq_csInfproof · cited by 1
- csInf_unionproof · cited by 0
- csInf_insertproof · cited by 0
- IsGLB.ciInf_eqproof · cited by 0
- IsGLB.ciInf_set_eqproof · cited by 0
- csInf_Iocproof · cited by 0