Theorems · Theorem · order theory
sInf_singleton
∀ {α : Type u_1} [inst : CompleteSemilatticeInf α] {a : α}, sInf {a} = a- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 11 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 · cited by 53,352
- InfSet.sInfstatement · cited by 935
- CompleteSemilatticeInfstatement and proof · cited by 19
- IsGLB.sInf_eqproof · cited by 14
- isGLB_singletonproof · cited by 7
Cited by8
Results whose statement or proof uses this declaration.
- Set.sInter_singletonproof · cited by 11
- iInf_constproof · cited by 9
- Ring.krullDimLE_zero_and_isLocalRing_tfaeproof · cited by 7
- IsArtinianRing.nilradical_pow_eq_iInfproof · cited by 3
- continuousSMul_sInfproof · cited by 2
- continuousVAdd_sInfproof · cited by 1
- sInf_zeroproof · cited by 0
- sInf_oneproof · cited by 0