Theorems · Theorem · commutative algebra
IsArtinian.finite_of_linearIndependent
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Nontrivial R]
[h : IsArtinian R M] {s : Set M}, LinearIndependent R Subtype.val → s.Finite- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Elemproof · cited by 7,166
- Bot.botproof · cited by 4,720
- Nontrivialstatement and proof · cited by 2,416
- Set.Finitestatement · cited by 1,814
- Submodule.spanproof · cited by 1,504
- LinearIndependentstatement and proof · cited by 560
- IsArtinianstatement and proof · cited by 69
- LinearIndependent.ne_zeroproof · cited by 20
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