Theorems · Definition · order theory
Sublattice.carrier
{α : Type u_2} → [inst : Lattice α] → Sublattice α → Set αThe underlying set of a sublattice. Do not use directly. Instead, use the coercion
Sublattice α → Set α, which Lean should automatically insert for you in most cases.
- Defined in
- Mathlib.Order.Sublattice
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- Lattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Latticestatement and proof · cited by 916
- Sublatticestatement and proof · cited by 225
Cited by33
Results whose statement or proof uses this declaration.
- Sublattice.supClosed'statement · cited by 2
- Sublattice.infClosed'statement · cited by 2
- CompleteSublattice.sInfClosed'statement · cited by 2
- CompleteSublattice.sSupClosed'statement · cited by 2
- CompleteSublattice.top_memproof · cited by 1
- BooleanSubalgebra.mk.injstatement and proof · cited by 1
- BooleanSubalgebra.mk.noConfusionstatement and proof · cited by 1
- BooleanSubalgebra.bot_mem'statement · cited by 1
- CompleteSublattice.mk.injstatement and proof · cited by 1
- CompleteSublattice.mk.noConfusionstatement and proof · cited by 1
- BooleanSubalgebra.compl_mem'statement · cited by 1
- BooleanSubalgebra.mem_carrierstatement · cited by 0