Theorems · Theorem · order theory
Order.Ideal.isPrime_iff_mem_or_compl_mem
∀ {P : Type u_1} [inst : BooleanAlgebra P] {I : Order.Ideal P} [I.IsProper], I.IsPrime ↔ ∀ {x : P}, x ∈ I ∨ xᶜ ∈ I- Defined in
- Mathlib.Order.PrimeIdeal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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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.IsProperstatement and proof · cited by 23
- Order.Ideal.IsPrimestatement and proof · cited by 11
- Order.Ideal.IsPrime.mem_or_compl_memproof · cited by 2
- Order.Ideal.isPrime_of_mem_or_compl_memproof · cited by 1
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