Theorems · Theorem · order theory
le_iInf
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {f : ι → α} {a : α}, (∀ (i : ι), a ≤ f i) → a ≤ iInf f- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 102 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 45 definitions · uses no axioms
- Assumes
- CompleteLattice
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.
- Set.rangeproof · cited by 4,705
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- le_sInfproof · cited by 51
Cited by102
Results whose statement or proof uses this declaration.
- le_iInf₂proof · cited by 67
- iInf_posproof · cited by 31
- iInf_monoproof · cited by 29
- iInf_negproof · cited by 27
- Finset.inf_eq_iInfproof · cited by 19
- Set.subset_iInterproof · cited by 17
- iInf_andproof · cited by 15
- iInf_commproof · cited by 12
- iInf_inf_eqproof · cited by 12
- iInf_subtypeproof · cited by 12
- iInf_mono'proof · cited by 10
- Filter.HasBasis.exists_antitone_subbasisproof · cited by 8