Theorems · Theorem · commutative algebra
Submodule.spanRank_span_of_linearIndepOn
∀ {R : Type u_1} {M : Type u} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [RankCondition R]
(s : Set M), LinearIndepOn R id s → (Submodule.span R s).spanRank = Cardinal.mk ↑s- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Elemstatement · cited by 7,166
- Cardinalstatement · cited by 2,598
- Submodule.spanstatement and proof · cited by 1,504
- Cardinal.mkstatement · cited by 942
- Subtype.val_injectiveproof · cited by 232
- LinearIndepOnstatement and proof · cited by 211
- Subtype.range_coe_subtypeproof · cited by 170
- Submodule.spanRankstatement and proof · cited by 61
Cited by1
Results whose statement or proof uses this declaration.
- Module.Basis.mk_eq_spanRankproof · cited by 1