Theorems · Theorem · linear algebra
exists_linearIndependent
∀ (K : Type u_3) {V : Type u} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] (t : Set V),
∃ b ⊆ t, Submodule.span K b = Submodule.span K t ∧ LinearIndependent K Subtype.val- Cited by
- 6 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coeproof · cited by 8,199
- Submodulestatement · cited by 7,192
- Submodule.spanstatement and proof · cited by 1,504
- DivisionRingstatement and proof · cited by 1,062
- LinearIndependentstatement · cited by 560
- LinearIndepOnproof · cited by 211
- Submodule.span_monoproof · cited by 85
- Set.empty_subsetproof · cited by 70
- Submodule.span_eq_of_leproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- ZLattice.rankproof · cited by 5
- Submodule.exists_finset_span_eq_linearIndepOnproof · cited by 2
- exists_linearIndependent'proof · cited by 1
- ZLattice.FGproof · cited by 1
- LinearMap.exists_basis_basis_of_span_eq_top_of_mem_algebraMapproof · cited by 1
- exists_affineIndependentproof · cited by 1