Theorems · Theorem · order theory
Set.Ici.isAtom_iff
∀ {α : Type u_2} [inst : PartialOrder α] {a : α} {b : ↑(Set.Ici a)}, IsAtom b ↔ a ⋖ ↑b- Defined in
- Mathlib.Order.Atoms
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrder
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- PartialOrderstatement and proof · cited by 6,410
- Set.Icistatement and proof · cited by 1,070
- CovBystatement and proof · cited by 290
- Subtype.range_coe_subtypeproof · cited by 170
- Set.OrdConnectedproof · cited by 161
- IsAtomstatement · cited by 130
- OrderEmbedding.subtypeproof · cited by 15
- Set.OrdConnected.apply_covBy_apply_iffproof · cited by 8
- bot_covBy_iffproof · cited by 4
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