Theorems · Theorem · order theory
Order.Ideal.IsPrime.compl_mem_of_notMem
∀ {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
- 0 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- BooleanAlgebra
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Cites5
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
- Order.Ideal.IsPrime.mem_or_compl_memproof · cited by 2
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