Theorems · Theorem · order theory
iSup_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
- 49 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.
- Bot.botstatement · cited by 4,720
- iSupstatement · cited by 2,415
- le_antisymmproof · cited by 2,068
- CompleteLatticestatement and proof · cited by 1,048
- bot_leproof · cited by 306
- iSup_leproof · cited by 190
Cited by49
Results whose statement or proof uses this declaration.
- Submodule.iSup_torsionBySet_ideal_eq_torsionBySet_iInfproof · cited by 5
- OrdinalApprox.lfpApprox_zeroproof · cited by 4
- Order.Ideal.biSup_mem_iffproof · cited by 3
- MeasureTheory.exists_isSigmaFiniteSet_measure_geproof · cited by 3
- SSet.Subcomplex.Pairing.RankFunction.filtration_botproof · cited by 3
- iSupIndep_iff_finsetSum_eq_zero_imp_eq_zeroproof · cited by 3
- DirectedOn.inf_sSup_eqproof · cited by 3
- MeasureTheory.OuterMeasure.le_boundedByproof · cited by 3
- MeasureTheory.OuterMeasure.boundedBy_caratheodoryproof · cited by 2
- tprod_iSup_decode₂proof · cited by 2
- AlgebraicGeometry.compact_open_induction_onproof · cited by 2
- Set.Finite.iInf_biSup_of_monotoneproof · cited by 2