Theorems · Theorem · order theory
isGLB_iff_sInf_eq
∀ {α : Type u_1} [inst : CompleteSemilatticeInf α] {s : Set α} {a : α}, IsGLB s a ↔ sInf s = a- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- CompleteSemilatticeInf
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.
- Setstatement and proof · cited by 53,352
- InfSet.sInfstatement and proof · cited by 935
- IsGLBstatement · cited by 213
- isGLB_sInfproof · cited by 23
- CompleteSemilatticeInfstatement and proof · cited by 19
- IsGLB.uniqueproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- IsGLB.sInf_eqproof · cited by 14