Theorems · Theorem · order theory
iInf_le
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] (f : ι → α) (i : ι), iInf f ≤ f i- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 104 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 44 definitions · uses no axioms
- Assumes
- CompleteLattice
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.
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- sInf_leproof · cited by 110
Cited by105
Results whose statement or proof uses this declaration.
- iInf_le_of_leproof · cited by 62
- iInf₂_leproof · cited by 45
- Set.iInter_subsetproof · cited by 39
- iInf_posproof · cited by 31
- Filter.mem_iInf_of_memproof · cited by 22
- Finset.inf_eq_iInfproof · cited by 19
- iInf_andproof · cited by 15
- iInf_commproof · cited by 12
- iInf_inf_eqproof · cited by 12
- iInf_subtypeproof · cited by 12
- Filter.HasBasis.exists_antitone_subbasisproof · cited by 8
- MeasureTheory.inducedOuterMeasure_eq_iInfproof · cited by 7