Theorems · Theorem · order theory
sInf_le_of_le
∀ {α : Type u_1} [inst : CompleteSemilatticeInf α] {s : Set α} {a b : α}, b ∈ s → b ≤ a → sInf s ≤ a- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 3 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
- sInf_leproof · cited by 110
- ge_transproof · cited by 34
- CompleteSemilatticeInfstatement and proof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.map_sInfproof · cited by 3
- Filter.limsup_eq_sInf_sSupproof · cited by 1
- DividedPowers.SubDPIdeal.span_carrier_eq_dpow_spanproof · cited by 0