Theorems · Theorem · linear algebra
exists_finset_linearIndependent_of_le_rank
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {n : ℕ},
↑n ≤ Module.rank R M → ∃ s, s.card = n ∧ LinearIndepOn R id ↑s- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Finsetstatement · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement · cited by 8,199
- Fintypeproof · cited by 7,736
- Set.Elemproof · cited by 7,166
- Finiteproof · cited by 3,029
- Cardinalstatement and proof · cited by 2,598
- iSupproof · cited by 2,415
- Finset.cardstatement · cited by 2,327
Cited by3
Results whose statement or proof uses this declaration.
- exists_finset_linearIndependent_of_le_finrankproof · cited by 2
- exists_linearIndependent_of_le_rankproof · cited by 1
- natCast_le_rank_iff_finsetproof · cited by 0