Theorems · Theorem · order theory
OrderEmbedding.supIrredLowerSet_apply
∀ {α : Type u_1} [inst : PartialOrder α] (a : α), OrderEmbedding.supIrredLowerSet a = ⟨LowerSet.Iic a, ⋯⟩- Defined in
- Mathlib.Order.Birkhoff
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrder
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Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- OrderEmbeddingstatement · cited by 619
- LowerSetstatement · cited by 230
- LowerSet.Iicstatement · cited by 37
- SupIrredstatement · cited by 34
- LowerSet.supIrred_Iicstatement · cited by 4
- OrderEmbedding.supIrredLowerSetstatement · cited by 2
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