Theorems · Theorem · order theory
Lattice.mem_ideal_sup_principal
∀ {α : Type u_1} [inst : Lattice α] (a b : α) (J : Order.Ideal α), b ∈ J ⊔ Order.Ideal.principal a ↔ ∃ j ∈ J, b ≤ j ⊔ a- Defined in
- Mathlib.Order.PrimeSeparator
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- Lattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_reflproof · cited by 2,061
- le_transproof · cited by 985
- Latticestatement and proof · cited by 916
- Order.Idealstatement and proof · cited by 102
- sup_le_sup_leftproof · cited by 20
- Order.Ideal.principalstatement and proof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- DistribLattice.prime_ideal_of_disjoint_filter_idealproof · cited by 0
- DistribLattice.mem_ideal_sup_principalproof · cited by 0