Theorems · Theorem · order theory
inf_le_of_left_le
∀ {α : Type u} [inst : SemilatticeInf α] {a b c : α}, a ≤ c → a ⊓ b ≤ c- Defined in
- Mathlib.Order.Lattice
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 5 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.
- SemilatticeInfstatement and proof · cited by 634
- inf_le_leftproof · cited by 286
- ge_transproof · cited by 34
Cited by17
Results whose statement or proof uses this declaration.
- inf_le_infproof · cited by 54
- iInf_orproof · cited by 5
- IsGLB.unionproof · cited by 4
- min_le_of_left_leproof · cited by 3
- bihimp_inf_supproof · cited by 2
- le_symmDiff_iff_leftproof · cited by 2
- Finset.Shatters.mono_rightproof · cited by 1
- BddBelow.range_iInf_of_iUnion_rangeproof · cited by 1
- Disjoint.of_disjoint_inf_of_leproof · cited by 1
- principal_inter_le_nhdsSetWithinproof · cited by 0
- IsCompact.adherence_nhdsetproof · cited by 0
- nhdsSetWithin_prod_leproof · cited by 0