Theorems · Theorem · order theory
countableSupClosed_preimage_toDual
∀ {α : Type u_2} [inst : LE α] {s : Set αᵒᵈ}, CountableSupClosed (⇑OrderDual.toDual ⁻¹' s) ↔ CountableInfClosed s- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
- Assumes
- LE
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Cites10
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
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Set.preimagestatement and proof · cited by 4,946
- OrderDualstatement and proof · cited by 927
- OrderDual.toDualstatement and proof · cited by 481
- CountableInfClosedstatement and proof · cited by 27
- CountableSupClosedstatement and proof · cited by 27
- CountableSupClosed.isLUB_memproof · cited by 10
- CountableInfClosed.isGLB_memproof · cited by 10
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