Theorems · Theorem · order theory
IsGLB.sInf_eq
∀ {α : Type u_1} [inst : CompleteSemilatticeInf α] {s : Set α} {a : α}, IsGLB s a → sInf s = aAlias of the forward direction of isGLB_iff_sInf_eq.
- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- CompleteSemilatticeInf
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
- IsGLBstatement · cited by 213
- CompleteSemilatticeInfstatement and proof · cited by 19
- isGLB_iff_sInf_eqproof · cited by 1
Cited by14
Results whose statement or proof uses this declaration.
- sInf_emptyproof · cited by 12
- sInf_singletonproof · cited by 8
- sInf_image2_eq_sInf_sInfproof · cited by 5
- sInf_pairproof · cited by 5
- sInf_insertproof · cited by 4
- sInf_univproof · cited by 3
- RightOrdContinuous.map_sInf'proof · cited by 2
- sInf_unionproof · cited by 1
- sdiff_eq_sInfproof · cited by 1
- IsGLB.iInf_eqproof · cited by 1
- Ideal.homogeneousHull_eq_sInfproof · cited by 0
- Convex.toCone_eq_sInfproof · cited by 0