Theorems · Theorem · linear algebra
rank_span_set
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
{s : Set M}, LinearIndepOn R id s → Module.rank R ↥(Submodule.span R s) = Cardinal.mk ↑s- Cited by
- 4 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement · cited by 7,192
- Set.Elemstatement and proof · cited by 7,166
- Cardinalstatement · cited by 2,598
- Submodule.spanstatement and proof · cited by 1,504
- Cardinal.mkstatement and proof · cited by 942
- Module.rankstatement and proof · cited by 496
- StrongRankConditionstatement and proof · cited by 286
- LinearIndepOnstatement and proof · cited by 211
Cited by4
Results whose statement or proof uses this declaration.
- finrank_span_set_eq_cardproof · cited by 4
- Submodule.exists_finset_span_eq_linearIndepOnproof · cited by 2
- exists_linearIndepOn_of_lt_rankproof · cited by 1
- Subalgebra.rank_botproof · cited by 1