Theorems · Theorem · order theory
le_iInf_iff
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {f : ι → α} {a : α}, a ≤ iInf f ↔ ∀ (i : ι), a ≤ f i- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Set.forall_mem_rangeproof · cited by 135
- le_isGLB_iffproof · cited by 17
- isGLB_iInfproof · cited by 7
Cited by30
Results whose statement or proof uses this declaration.
- OrderIso.map_iInfproof · cited by 25
- iInf_prodproof · cited by 7
- le_iInf₂_iffproof · cited by 7
- iInf_optionproof · cited by 7
- Module.map_jacobson_of_ker_leproof · cited by 6
- Module.le_comap_jacobsonproof · cited by 6
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesproof · cited by 5
- Set.subset_iInter_iffproof · cited by 4
- iInf_sigmaproof · cited by 3
- contentRegular_rieszContentproof · cited by 3
- iInf_psigmaproof · cited by 2
- iInf_ge_eq_iInf_nat_addproof · cited by 2