Theorems · Theorem · order theory
subset_countableSupClosure
∀ {α : Type u_2} {s : Set α} [inst : Preorder α], s ⊆ countableSupClosure s- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Preorderstatement and proof · cited by 7,952
- ClosureOperatorstatement · cited by 371
- countableSupClosurestatement and proof · cited by 21
- ClosureOperator.le_closureproof · cited by 19
Cited by7
Results whose statement or proof uses this declaration.
- mem_countableSupClosure_iff_iSupproof · cited by 1
- upperBounds_countableSupClosureproof · cited by 1
- countableSupClosure_prodproof · cited by 0
- iSup_mem_countableSupClosureproof · cited by 0
- finsetSup'_mem_countableSupClosureproof · cited by 0
- countableSupClosure_eq_sInterproof · cited by 0
- sup_mem_countableSupClosureproof · cited by 0