Theorems · Theorem · commutative algebra
Submodule.rank_eq_spanRank_of_free
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Free R M]
[StrongRankCondition R], Module.rank R M = ⊤.spanRank- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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 and proof · cited by 9,680
- Submodulestatement · cited by 7,192
- Set.Elemproof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Cardinalstatement and proof · cited by 2,598
- Nontrivialproof · cited by 2,416
- Module.Basisproof · cited by 1,477
- Cardinal.mkproof · cited by 942
Cited by2
Results whose statement or proof uses this declaration.
- Module.finrank_eq_spanFinrank_of_freeproof · cited by 2
- IsLocalRing.rank_cotangentSpace_eq_spanrank_maximalIdeal_of_fgproof · cited by 1