Theorems · Theorem · order theory
supClosure_infClosure
∀ {α : Type u_3} [inst : DistribLattice α] (s : Set α), supClosure (infClosure s) = latticeClosure s- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 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.
Cites21
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
- LE.le.transproof · cited by 3,151
- le_antisymmproof · cited by 2,068
- ClosureOperatorstatement · cited by 371
- DistribLatticestatement and proof · cited by 150
- supClosurestatement · cited by 33
- latticeClosurestatement · cited by 24
- infClosurestatement · cited by 21
- IsSublattice.infClosedproof · cited by 15
- IsSublattice.supClosedproof · cited by 15
- subset_supClosureproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- Set.Finite.latticeClosureproof · cited by 1
- latticeClosure_prodproof · cited by 0