Theorems · Theorem · linear algebra
linearIndependent_iff_card_le_finrank_span
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [OrzechProperty R] [inst_2 : AddCommMonoid M] [inst_3 : Module R M]
[Nontrivial R] {ι : Type u_3} [inst_5 : Fintype ι] {b : ι → M},
LinearIndependent R b ↔ Fintype.card ι ≤ Set.finrank R (Set.range b)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Set.rangestatement and proof · cited by 4,705
- Nontrivialstatement and proof · cited by 2,416
- Fintype.cardstatement and proof · cited by 1,386
- LinearIndependentstatement · cited by 560
- LE.le.ge_iff_eq'proof · cited by 50
- OrzechPropertystatement and proof · cited by 16
- Set.finrankstatement and proof · cited by 9
- linearIndependent_iff_card_eq_finrank_spanproof · cited by 5
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