Theorems · Theorem · order theory
inf_le_inf_right
∀ {α : Type u} [inst : SemilatticeInf α] {a b : α} (c : α), b ≤ a → b ⊓ c ≤ a ⊓ c- Defined in
- Mathlib.Order.Lattice
- Cited by
- 23 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 by23
Results whose statement or proof uses this declaration.
- IsOpenMap.clusterPt_comapproof · cited by 3
- Disjoint.le_of_codisjointproof · cited by 3
- Disjoint.disjoint_sup_right_of_disjoint_sup_leftproof · cited by 3
- closure_inter_open_nonempty_iffproof · cited by 2
- strictMono_inf_prod_supproof · cited by 2
- equicontinuousWithinAt_iInf_domproof · cited by 2
- LinearMap.comap_leq_ker_subToSupQuotientproof · cited by 2
- iSup_inf_le_sSup_infproof · cited by 1
- min_le_min_rightproof · cited by 1
- nhdsLE_eq_iInf_inf_principalproof · cited by 1
- nhdsGE_eq_iInf_inf_principalproof · cited by 1
- Specializes.clusterPtproof · cited by 1