Theorems · Theorem · order theory
Order.Ideal.IsProper.notMem_of_compl_mem
∀ {P : Type u_1} [inst : BooleanAlgebra P] {x : P} {I : Order.Ideal P}, I.IsProper → xᶜ ∈ I → x ∉ I- Defined in
- Mathlib.Order.Ideal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- BooleanAlgebra
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.
- Compl.complstatement and proof · cited by 2,925
- BooleanAlgebrastatement and proof · cited by 300
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.IsProperstatement and proof · cited by 23
- Order.Ideal.sup_memproof · cited by 5
- sup_compl_eq_topproof · cited by 4
- Order.Ideal.IsProper.top_notMemproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Order.Ideal.IsProper.notMem_or_compl_notMemproof · cited by 0