Theorems · Theorem · order theory
sInf_le
∀ {α : Type u_1} [inst : CompleteSemilatticeInf α] {s : Set α} {a : α}, a ∈ s → sInf s ≤ a- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 110 results in Mathlib
- Foundations
- Depth 9 from the axioms, rests on 23 definitions · uses no axioms
- Assumes
- CompleteSemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- isGLB_sInfproof · cited by 23
- CompleteSemilatticeInfstatement and proof · cited by 19
Cited by110
Results whose statement or proof uses this declaration.
- iInf_leproof · cited by 104
- ENNReal.inv_topproof · cited by 36
- AddSubmonoid.closure_leproof · cited by 35
- Subgroup.closure_leproof · cited by 31
- AddSubgroup.closure_leproof · cited by 30
- Set.sInter_subset_of_memproof · cited by 28
- Submonoid.closure_leproof · cited by 27
- ENNReal.coe_invproof · cited by 27
- sInf_eq_iInfproof · cited by 22
- Ideal.radical_eq_sInfproof · cited by 21
- Subring.closure_leproof · cited by 14
- Ideal.exists_minimalPrimes_leproof · cited by 14