Theorems · Theorem · order theory
iInf_iInf_eq_left
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {b : β} {f : (x : β) → x = b → α},
⨅ x, ⨅ (h : x = b), f x h = f b ⋯- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement · cited by 1,690
- le_rflproof · cited by 1,558
- CompleteLatticestatement and proof · cited by 1,048
- le_iInf₂proof · cited by 67
- ge_antisymmproof · cited by 51
- iInf₂_leproof · cited by 45
Cited by12
Results whose statement or proof uses this declaration.
- Set.iInter_iInter_eq_leftproof · cited by 18
- nhds_eq_orderproof · cited by 9
- iInf_insertproof · cited by 5
- PrimeSpectrum.vanishingIdeal_singletonproof · cited by 5
- iInf_singletonproof · cited by 5
- iInf_split_singleproof · cited by 2
- Filter.lift_topproof · cited by 2
- CompleteLatticeHom.apply_limsup_iterateproof · cited by 2
- ProjectiveSpectrum.vanishingIdeal_singletonproof · cited by 1
- Metric.coveringNumber_emptyproof · cited by 1
- Finset.iInf_singletonproof · cited by 1
- Ideal.iSup_iInf_eq_top_iff_pairwiseproof · cited by 1