Theorems · Theorem · linear algebra
Submodule.span_range_inclusion_restrictScalars_eq_top
∀ (R : Type u_1) {M : Type u_4} (S : Type u_7) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(s : Set M) [inst_3 : Semiring S] [inst_4 : SMul R S] [inst_5 : Module S M] [inst_6 : IsScalarTower R S M],
Submodule.span S (Set.range ⇑(Submodule.inclusion ⋯)) = ⊤- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · 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 · cited by 9,680
- Submodulestatement · cited by 7,192
- Set.rangestatement · cited by 4,705
- IsScalarTowerstatement and proof · cited by 3,896
- Submodule.spanstatement and proof · cited by 1,504
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