Theorems · Theorem · commutative algebra
Module.finrank_eq_spanFinrank_of_free
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[StrongRankCondition R] [Module.Free R M], Module.finrank R M = ⊤.spanFinrank- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Module.finrankstatement · cited by 1,770
- Module.Freestatement and proof · cited by 597
- StrongRankConditionstatement and proof · cited by 286
- Cardinal.toNatproof · cited by 153
- Submodule.spanRankproof · cited by 61
- Submodule.spanFinrankstatement · cited by 49
Cited by2
Results whose statement or proof uses this declaration.
- minpoly.natDegree_leproof · cited by 6
- IsLocalRing.spanFinrank_eq_finrank_quotientproof · cited by 1