Theorems · Theorem · order theory
SupClosed.infClosure
∀ {α : Type u_3} [inst : DistribLattice α] {s : Set α}, SupClosed s → SupClosed (infClosure s)- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DistribLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- SProd.sprodproof · cited by 1,750
- Finset.Nonemptyproof · cited by 1,001
- ClosureOperatorstatement · cited by 371
- DistribLatticestatement and proof · cited by 150
- Finset.inf'proof · cited by 117
- SupClosedstatement and proof · cited by 57
- Finset.mem_productproof · cited by 48
- infClosurestatement and proof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- infClosure_supClosureproof · cited by 0