Theorems · Theorem · linear algebra
Submodule.subset_span
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {s : Set M},
s ⊆ ↑(Submodule.span R s)- Defined in
- Mathlib.LinearAlgebra.Span.Defs
- Cited by
- 234 results in Mathlib
- Foundations
- Depth 19 from the axioms, rests on 103 definitions · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Submodule.spanstatement · cited by 1,504
- Submodule.mem_spanproof · cited by 5
Cited by234
Results whose statement or proof uses this declaration.
- Submodule.span_leproof · cited by 164
- Ideal.subset_spanproof · cited by 86
- Submodule.span_monoproof · cited by 85
- Submodule.map_spanproof · cited by 84
- Submodule.span_inductionstatement and proof · cited by 77
- Submodule.mem_span_singletonproof · cited by 61
- Submodule.mem_span_singleton_selfproof · cited by 59
- Submodule.span_eqproof · cited by 26
- Finsupp.range_linearCombinationproof · cited by 24
- Submodule.span_span_of_towerproof · cited by 18
- Algebra.adjoin_eq_spanproof · cited by 13
- NonUnitalAlgebra.subset_adjoinproof · cited by 13
Showing the 200 most cited of 234.