Theorems · Theorem · commutative algebra
isArtinian_of_le
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{s t : Submodule R M} [IsArtinian R ↥t], s ≤ t → IsArtinian R ↥s- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Submodule.inclusionproof · cited by 74
- IsArtinianstatement and proof · cited by 69
- Submodule.inclusion_injectiveproof · cited by 15
- isArtinian_of_injectiveproof · cited by 2
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