Theorems · Theorem · order theory
Order.Ideal.isProper_of_notMem
∀ {P : Type u_1} [inst : LE P] {I : Order.Ideal P} {p : P}, p ∉ I → I.IsProper- Defined in
- Mathlib.Order.Ideal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- LE
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.
- Setproof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Set.univproof · cited by 3,945
- Set.mem_univproof · cited by 416
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.IsProperstatement · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Order.Ideal.PrimePair.I_isProperproof · cited by 1
- DistribLattice.prime_ideal_of_disjoint_filter_idealproof · cited by 0