Theorems · Theorem · linear algebra
Submodule.span_range_inclusionSpan
∀ {R : Type u_1} {M : Type u_4} (S : Type u_7) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : Semiring S] [inst_4 : SMul R S] [inst_5 : Module S M] [inst_6 : IsScalarTower R S M] (p : Submodule R M),
Submodule.span S (Set.range ⇑(Submodule.inclusionSpan S p)) = ⊤- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.imageproof · cited by 5,609
- Set.rangestatement and proof · cited by 4,705
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.IsPerfPair.restrictScalars_of_fieldproof · cited by 0