Theorems · Theorem · order theory
inf_mem_infClosure
∀ {α : Type u_3} [inst : SemilatticeInf α] {s : Set α} {a b : α}, a ∈ s → b ∈ s → a ⊓ b ∈ infClosure s- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 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
- infClosurestatement · cited by 21
- subset_infClosureproof · cited by 6
- infClosed_infClosureproof · cited by 5
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