Theorems · Theorem · order theory
Order.Ideal.IsPrime.mem_or_compl_mem
∀ {P : Type u_1} [inst : BooleanAlgebra P] {x : P} {I : Order.Ideal P}, I.IsPrime → x ∈ I ∨ xᶜ ∈ I- Defined in
- Mathlib.Order.PrimeIdeal
- Cited by
- 2 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 · cited by 2,925
- BooleanAlgebrastatement and proof · cited by 300
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.IsPrimestatement and proof · cited by 11
- inf_compl_eq_botproof · cited by 4
- Order.Ideal.IsPrime.mem_or_memproof · cited by 2
- Order.Ideal.bot_memproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Order.Ideal.isPrime_iff_mem_or_compl_memproof · cited by 0
- Order.Ideal.IsPrime.compl_mem_of_notMemproof · cited by 0