Theorems · Theorem · linear algebra
finite_of_span_finite_eq_top_finsupp
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Nontrivial M]
{ι : Type u_1} {s : Set (ι →₀ M)}, s.Finite → Submodule.span R s = ⊤ → Finite ι- Defined in
- Mathlib.LinearAlgebra.Basis.Cardinality
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Submodulestatement · cited by 7,192
- Finsuppstatement and proof · cited by 5,255
- Set.univproof · cited by 3,945
- LE.le.transproof · cited by 3,151
- Finitestatement · cited by 3,029
- Set.iUnionproof · cited by 2,483
Cited by2
Results whose statement or proof uses this declaration.
- basis_finite_of_finite_spansproof · cited by 4
- Module.finite_finsupp_iffproof · cited by 0