Theorems · Theorem · order theory
iSup_pos
∀ {α : Type u_1} [inst : CompleteLattice α] {p : Prop} {f : p → α} (hp : p), ⨆ (h : p), f h = f hp- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 61 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.
- iSupstatement · cited by 2,415
- le_antisymmproof · cited by 2,068
- le_rflproof · cited by 1,558
- CompleteLatticestatement and proof · cited by 1,048
- le_iSupproof · cited by 207
- iSup_leproof · cited by 190
Cited by61
Results whose statement or proof uses this declaration.
- iSup_univproof · cited by 8
- iSup_splitproof · cited by 6
- Module.End.genEigenspace_top_eq_maxUnifEigenspaceIndexproof · cited by 5
- MeasureTheory.Measure.nullSingletonClass_hausdorffproof · cited by 5
- Submodule.fg_iSupproof · cited by 3
- iSupIndep.pairwiseDisjointproof · cited by 3
- iSupIndep_iff_finsetSum_eq_zero_imp_eq_zeroproof · cited by 3
- Nat.iSup_lt_succ'proof · cited by 3
- MeasureTheory.OuterMeasure.le_boundedByproof · cited by 3
- iSup_fin_threeproof · cited by 3
- Finset.sup_univ_eq_iSupproof · cited by 3
- MeasureTheory.OuterMeasure.boundedBy_caratheodoryproof · cited by 2