Theorems · Theorem · order theory
sup_mem_supClosure
∀ {α : Type u_3} [inst : SemilatticeSup α] {s : Set α} {a b : α}, a ∈ s → b ∈ s → a ⊔ b ∈ supClosure s- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- SemilatticeSupstatement and proof · cited by 785
- ClosureOperatorstatement · cited by 371
- supClosurestatement · cited by 33
- subset_supClosureproof · cited by 11
- supClosed_supClosureproof · cited by 8
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