Theorems · Theorem · order theory
inf_le_inf_left
∀ {α : Type u} [inst : SemilatticeInf α] {a b : α} (c : α), b ≤ a → c ⊓ b ≤ c ⊓ a- Defined in
- Mathlib.Order.Lattice
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_rflproof · cited by 1,558
- SemilatticeInfstatement and proof · cited by 634
- inf_le_infproof · cited by 54
Cited by25
Results whose statement or proof uses this declaration.
- nhdsWithin_monoproof · cited by 82
- ClusterPt.monoproof · cited by 30
- Filter.push_pullproof · cited by 7
- AccPt.monoproof · cited by 7
- LowerSemicontinuousOn.exists_isMinOnproof · cited by 6
- inf_sSup_eq_iSup_inf_sup_finsetproof · cited by 4
- le_of_inf_le_sup_leproof · cited by 4
- nhdsWithin_restrict''proof · cited by 4
- BoxIntegral.Prepartition.restrict_monoproof · cited by 3
- inf_sup_assoc_of_leproof · cited by 3
- iSup_inf_le_inf_sSupproof · cited by 2
- PhragmenLindelof.right_half_plane_of_tendsto_zero_on_realproof · cited by 2