Theorems · Theorem · order theory
latticeClosure_eq_self
∀ {α : Type u_3} [inst : Lattice α] {s : Set α}, latticeClosure s = s ↔ IsSublattice s- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Lattice
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
- Latticestatement and proof · cited by 916
- ClosureOperatorstatement · cited by 371
- IsSublatticestatement · cited by 28
- latticeClosurestatement and proof · cited by 24
- ClosureOperator.isClosed_iffproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- IsSublattice.latticeClosure_eqproof · cited by 0