Theorems · Theorem · linear algebra
finrank_span_finset_eq_card
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
{s : Finset M}, LinearIndepOn R id ↑s → Module.finrank R ↥(Submodule.span R ↑s) = s.card- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Semiringstatement and proof · cited by 13,802
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- Finset.cardstatement and proof · cited by 2,327
- Module.finrankstatement and proof · cited by 1,770
- Submodule.spanstatement and proof · cited by 1,504
- Finset.extproof · cited by 565
- StrongRankConditionstatement and proof · cited by 286
- Set.toFinsetproof · cited by 217
Cited by1
Results whose statement or proof uses this declaration.
- AffineIndependent.finrank_vectorSpan_image_finsetproof · cited by 3