Theorems · Theorem · linear algebra
linearIndependent_subsingleton_index_iff
∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} [inst : Ring R] [IsDomain R] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] [Module.IsTorsionFree R M] [Subsingleton ι] (f : ι → M),
LinearIndependent R f ↔ ∀ (i : ι), f i ≠ 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- IsDomainstatement and proof · cited by 2,196
- IsEmptyproof · cited by 759
- Module.IsTorsionFreestatement and proof · cited by 600
- LinearIndependentstatement · cited by 560
- Uniqueproof · cited by 400
- isEmpty_or_nonemptyproof · cited by 269
- Unique.eq_defaultproof · cited by 38
- unique_iff_subsingleton_and_nonemptyproof · cited by 6
- linearIndependent_unique_iffproof · cited by 3
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