Theorems · Theorem · order theory
partialSups_add_one_eq_sup_disjointed
∀ {α : Type u_1} {ι : Type u_2} [inst : GeneralizedBooleanAlgebra α] [inst_1 : LinearOrder ι]
[inst_2 : LocallyFiniteOrderBot ι] [inst_3 : Add ι] [inst_4 : One ι] [SuccAddOrder ι] (f : ι → α) (i : ι),
(partialSups f) (i + 1) = (partialSups f) i ⊔ disjointed f (i + 1)- Defined in
- Mathlib.Algebra.Order.Disjointed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- LinearOrderstatement and proof · cited by 8,572
- le_antisymmproof · cited by 2,068
- le_transproof · cited by 985
- OrderHomstatement · cited by 934
- Order.succproof · cited by 633
- Finset.supproof · cited by 530
- IsMaxproof · cited by 372
- LocallyFiniteOrderBotstatement and proof · cited by 286
- le_sup_rightproof · cited by 242
- GeneralizedBooleanAlgebrastatement and proof · cited by 204
- Finset.Iioproof · cited by 147
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