Theorems · Theorem · order theory
iInf_neg
∀ {α : Type u_1} [inst : CompleteLattice α] {p : Prop} {f : p → α}, ¬p → ⨅ (h : p), f h = ⊤- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 11 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.
- Top.topstatement · cited by 9,680
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- le_topproof · cited by 411
- le_iInfproof · cited by 102
- ge_antisymmproof · cited by 51
Cited by27
Results whose statement or proof uses this declaration.
- Submodule.iSup_torsionBySet_ideal_eq_torsionBySet_iInfproof · cited by 5
- Ideal.sup_iInf_eq_topproof · cited by 5
- nhds_bot_orderproof · cited by 4
- nhds_top_orderproof · cited by 4
- Ideal.prod_eq_iInf_of_pairwise_isCoprimeproof · cited by 4
- Ideal.height_topproof · cited by 4
- Filter.iInf_principal_finsetproof · cited by 3
- iInf_emptysetproof · cited by 3
- iInf_diteproof · cited by 2
- MeasureTheory.OuterMeasure.ofFunction_eq_iInf_memproof · cited by 2
- iInf_eq_difproof · cited by 2
- Set.Finite.iSup_biInf_of_monotoneproof · cited by 2