Theorems · Theorem · order theory
inf_mem_countableInfClosure
∀ {α : Type u_2} {s : Set α} {a b : α} [inst : SemilatticeInf α], a ∈ s → b ∈ s → a ⊓ b ∈ countableInfClosure s- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInf
Around this declaration
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- SemilatticeInfstatement and proof · cited by 634
- ClosureOperatorstatement · cited by 371
- countableInfClosurestatement · cited by 21
- subset_countableInfClosureproof · cited by 7
- infClosed_countableInfClosureproof · cited by 2
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