Theorems · Theorem · linear algebra
Submodule.span_attach_biUnion
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : DecidableEq M] {α : Type u_9} (s : Finset α) (f : ↥s → Finset M),
Submodule.span R ↑(s.attach.biUnion f) = ⨆ x, Submodule.span R ↑(f x)- Defined in
- Mathlib.LinearAlgebra.Span.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- Set.iUnionproof · cited by 2,483
- iSupstatement and proof · cited by 2,415
- Submodule.spanstatement and proof · cited by 1,504
- Set.iUnion_congr_Propproof · cited by 374
- Finset.biUnionstatement · cited by 217
- Finset.attachstatement · cited by 168
Cited by2
Results whose statement or proof uses this declaration.
- Module.Finite.of_localizationSpan_finite'proof · cited by 2
- RingHom.finite_ofLocalizationSpanproof · cited by 0