Theorems · Theorem · commutative algebra
Module.Basis.mk_eq_spanRank
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [RankCondition R]
{ι : Type u_3} (v : Module.Basis ι R M), Cardinal.mk ↑(Set.range ⇑v) = ⊤.spanRank- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topstatement · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Set.Elemstatement and proof · cited by 7,166
- Set.rangestatement and proof · cited by 4,705
- Cardinalstatement and proof · cited by 2,598
- Module.Basisstatement and proof · cited by 1,477
- Cardinal.mkstatement and proof · cited by 942
- Submodule.spanRankstatement and proof · cited by 61
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.rank_eq_spanRank_of_freeproof · cited by 2