Theorems · Theorem · commutative algebra
Submodule.spanFinrank_top
∀ {R : Type u_1} {M : Type u} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (p : Submodule R M),
⊤.spanFinrank = p.spanFinrank- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Cardinal.toNatproof · cited by 153
- Submodule.spanRankproof · cited by 61
- Submodule.spanFinrankstatement · cited by 49
- Submodule.spanRank_topproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- TensorProduct.spanFinrank_top_eq_of_residueFieldproof · cited by 1
- TensorProduct.spanFinrank_top_le_of_fgproof · cited by 1