Theorems · Theorem · linear algebra
LinearIndependent.of_subsingleton
∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{v : ι → M} [IsDomain R] [Module.IsTorsionFree R M] [Subsingleton ι] (i : ι), v i ≠ 0 → LinearIndependent R v- Cited by
- 5 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Module.IsTorsionFreestatement and proof · cited by 600
- LinearIndependentstatement · cited by 560
- LinearIndependent.of_subsingleton'proof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- linearIndependent_unique_iffproof · cited by 3
- finrank_eq_one_iff_of_nonzeroproof · cited by 3
- exists_linearIndependent_pair_of_one_lt_rankproof · cited by 2
- Profinite.NobelingProof.GoodProducts.linearIndependentSingletonproof · cited by 1
- affineIndependent_of_neproof · cited by 1