Theorems · Definition · order theory
Order.Ideal.IsPrime.toPrimePair
{P : Type u_1} → [inst : Preorder P] → {I : Order.Ideal P} → I.IsPrime → Order.Ideal.PrimePair PCreate an element of type Order.Ideal.PrimePair from an ideal satisfying the predicate
Order.Ideal.IsPrime.
- Defined in
- Mathlib.Order.PrimeIdeal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.PrimePairstatement · cited by 12
- Order.Ideal.IsPrimestatement and proof · cited by 11
- Order.IsPFilter.toPFilterproof · cited by 1
- Order.Ideal.IsPrime.compl_filterproof · cited by 1
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