Theorems · Theorem · commutative algebra
Ideal.setOfPred_isPrincipal_wellFoundedOn_gt
∀ {α : Type u_1} [inst : CommSemiring α] [WfDvdMonoid α] [IsDomain α],
{I | Submodule.IsPrincipal I}.WellFoundedOn fun x1 x2 => x1 > x2The ascending chain condition on principal ideals holds in a WfDvdMonoid domain.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Set.ofPredstatement and proof · cited by 6,101
- Set.imageproof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- Set.univproof · cited by 3,945
- Set.extproof · cited by 2,266
- IsDomainstatement and proof · cited by 2,196
- Submodule.spanproof · cited by 1,504
- Ideal.spanproof · cited by 948
- Function.onFunproof · cited by 570
- Set.image_univproof · cited by 322
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.setOf_isPrincipal_wellFoundedOn_gtproof · cited by 0