Theorems · Theorem · linear algebra
linearIndependent_empty_type
∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} {v : ι → M} [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] [IsEmpty ι], LinearIndependent R v- Cited by
- 9 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- IsEmptystatement and proof · cited by 759
- LinearIndependentstatement · cited by 560
- Finsupp.linearCombinationproof · cited by 269
- Function.injective_of_subsingletonproof · cited by 17
Cited by9
Results whose statement or proof uses this declaration.
- linearIndepOn_emptyproof · cited by 5
- linearIndependent_emptyproof · cited by 4
- IsLocalizedModule.linearIndependent_liftproof · cited by 2
- linearIndependent_zero_iffproof · cited by 2
- bernsteinPolynomial.linearIndependent_auxproof · cited by 1
- Profinite.NobelingProof.GoodProducts.linearIndependentEmptyproof · cited by 1
- RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zeroproof · cited by 1
- FixedPoints.linearIndependent_smul_of_linearIndependentproof · cited by 1
- linearIndependent_powproof · cited by 0