Theorems · Theorem · linear algebra
exists_linearIndepOn_of_lt_rank
∀ {R : Type u_1} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[HasRankNullity.{u, u_1} R] [StrongRankCondition R] {s : Set M},
LinearIndepOn R id s → ∃ t, s ⊆ t ∧ Cardinal.mk ↑t = Module.rank R M ∧ LinearIndepOn R id t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Set.Elemstatement and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- Cardinalstatement and proof · cited by 2,598
- HasQuotient.Quotientproof · cited by 2,301
- Disjointproof · cited by 2,201
- add_commproof · cited by 1,535
- Submodule.spanproof · cited by 1,504
Cited by1
Results whose statement or proof uses this declaration.
- exists_linearIndependent_cons_of_lt_rankproof · cited by 2