Theorems · Inductive type · order theory
Sublattice
(α : Type u_2) → [Lattice α] → Type u_2
A sublattice of a lattice is a set containing the suprema and infima of any of its elements.
- Defined in
- Mathlib.Order.Sublattice
- Cited by
- 225 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- Lattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Latticestatement · cited by 916
Cited by269
Results whose statement or proof uses this declaration.
- Module.End.invtSubmodulestatement · cited by 93
- Sublattice.carrierstatement and proof · cited by 23
- Sublattice.mapstatement and proof · cited by 20
- Sublattice.comapstatement and proof · cited by 18
- Sublattice.prodstatement and proof · cited by 18
- RootPairing.invtRootSubmodulestatement · cited by 16
- Module.End.mem_invtSubmodulestatement · cited by 9
- Sublattice.pistatement and proof · cited by 9
- Sublattice.subtypestatement and proof · cited by 9
- LieAlgebra.IsKilling.invtSubmoduleToLieIdealstatement · cited by 7
- Representation.invtSubmodulestatement · cited by 7
- CompleteSublattice.toSublatticestatement · cited by 7
Showing the 200 most cited of 269.