Theorems · Theorem · order theory
iInf_and
∀ {α : Type u_1} [inst : CompleteLattice α] {p q : Prop} {s : p ∧ q → α}, iInf s = ⨅ (h₁ : p), ⨅ (h₂ : q), s ⋯- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 15 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- iInf_leproof · cited by 104
- le_iInfproof · cited by 102
- le_iInf₂proof · cited by 67
- ge_antisymmproof · cited by 51
- iInf₂_leproof · cited by 45
Cited by15
Results whose statement or proof uses this declaration.
- nhds_eq_orderproof · cited by 9
- Set.iInter_andproof · cited by 8
- Filter.nhds_eqproof · cited by 6
- iInf_and'proof · cited by 5
- ContinuousMap.nhds_compactOpenproof · cited by 4
- biInf_prodproof · cited by 4
- TopCat.Presheaf.EtaleSpace.eventually_nhdsproof · cited by 2
- Metric.infEDist_prodproof · cited by 2
- Finset.iInf_biUnionproof · cited by 1
- nhds_def'proof · cited by 1
- Filter.prod_defproof · cited by 1
- Filter.nhds_nhdsproof · cited by 1