Theorems · Theorem · linear algebra
Submodule.span_biUnion
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(s : Set (Submodule R M)), Submodule.span R (⋃ S ∈ s, ↑S) = sSup s- Defined in
- Mathlib.LinearAlgebra.Span.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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Cites12
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
- Set.iUnionstatement · cited by 2,483
- Submodule.spanstatement and proof · cited by 1,504
- SupSet.sSupstatement and proof · cited by 954
- Set.sUnion_imageproof · cited by 28
- Submodule.giproof · cited by 12
- GaloisInsertion.l_sSup_u_imageproof · cited by 4
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