Theorems · Theorem · linear algebra
LinearIndependent.setFinite
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
[Module.Finite R M] {b : Set M}, (LinearIndependent R fun (x : ↑b) => ↑x) → b.Finite- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Elemstatement and proof · cited by 7,166
- Set.Finitestatement · cited by 1,814
- Module.Finitestatement and proof · cited by 1,032
- LinearIndependentstatement and proof · cited by 560
- StrongRankConditionstatement and proof · cited by 286
- Cardinal.lt_aleph0_iff_set_finiteproof · cited by 7
- LinearIndependent.lt_aleph0_of_finiteproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Orthonormal.exists_orthonormalBasis_extensionproof · cited by 2
- ZLattice.FGproof · cited by 1