Theorems · Theorem · linear algebra
Submodule.span_eq
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(p : Submodule R M), Submodule.span R ↑p = p- Defined in
- Mathlib.LinearAlgebra.Span.Defs
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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.subset_spanproof · cited by 234
- Set.Subset.reflproof · cited by 66
- Submodule.span_eq_of_leproof · cited by 11
Cited by26
Results whose statement or proof uses this declaration.
- Submodule.mem_supproof · cited by 73
- Ideal.IsMaximal.isPrimeproof · cited by 53
- Submodule.span_coe_eq_restrictScalarsproof · cited by 13
- Submodule.ideal_span_singleton_smulproof · cited by 7
- Submodule.mem_span_mul_finite_of_mem_mulproof · cited by 3
- Submodule.map₂_eq_span_image2proof · cited by 3
- Submodule.iSup_eq_spanproof · cited by 3
- Ideal.Filtration.submodule_span_singleproof · cited by 2
- Submodule.map₂_span_singleton_eq_mapproof · cited by 2
- Submodule.span_spanproof · cited by 2
- Submodule.fg_iff_compactproof · cited by 1
- Submodule.pow_eq_span_pow_setproof · cited by 1