Theorems · Theorem · order theory
countableInfClosure_min
∀ {α : Type u_2} {s t : Set α} [inst : Preorder α], s ⊆ t → CountableInfClosed t → countableInfClosure s ⊆ t- Defined in
- Mathlib.Order.CountableSupClosed
- Cited by
- 3 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.
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
- Preorderstatement and proof · cited by 7,952
- ClosureOperatorstatement · cited by 371
- CountableInfClosedstatement and proof · cited by 27
- countableInfClosurestatement · cited by 21
- ClosureOperator.closure_minproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- mem_countableInfClosure_iff_iInfproof · cited by 1
- countableInfClosure_eq_sInterproof · cited by 0
- countableInfClosure_prodproof · cited by 0