Theorems · Theorem · order theory
exists_partialSups_eq
∀ {α : Type u_1} {ι : Type u_3} [inst : Preorder ι] [inst_1 : LocallyFiniteOrderBot ι] [inst_2 : LinearOrder α]
(f : ι → α) (i : ι), ∃ j ≤ i, (partialSups f) i = f j- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- LinearOrderstatement and proof · cited by 8,572
- Preorderstatement and proof · cited by 7,952
- le_antisymmproof · cited by 2,068
- le_rflproof · cited by 1,558
- OrderHomstatement · cited by 934
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Finset.Iicproof · cited by 280
- partialSupsstatement · cited by 67
- Finset.mem_Iicproof · cited by 42
- Finset.exists_max_imageproof · cited by 8
- le_partialSups_of_leproof · cited by 4
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