Theorems · Theorem · linear algebra
exists_finset_linearIndependent_of_le_finrank
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {n : ℕ},
n ≤ Module.finrank R M → ∃ s, s.card = n ∧ LinearIndependent R Subtype.val- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 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.
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
- Set.Elemproof · cited by 7,166
- Finset.cardstatement and proof · cited by 2,327
- Module.finrankstatement and proof · cited by 1,770
- LinearIndependentstatement and proof · cited by 560
- LE.le.trans_eqproof · cited by 328
- Nat.cast_leproof · cited by 159
- le_zero_iffproof · cited by 15
- Cardinal.cast_toNat_of_lt_aleph0proof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- exists_linearIndependent_of_le_finrankproof · cited by 2
- Submodule.exists_of_finrank_ltproof · cited by 0