Theorems · Theorem · linear algebra
AddSubmonoid.toNatSubmodule_closure
∀ {M : Type u_4} [inst : AddCommMonoid M] (s : Set M),
AddSubmonoid.toNatSubmodule (AddSubmonoid.closure s) = Submodule.span ℕ s- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
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Cites14
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
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement · cited by 7,192
- Submodule.spanstatement · cited by 1,504
- AddSubmonoidstatement · cited by 1,178
- OrderIsostatement · cited by 874
- Submodule.subset_spanproof · cited by 234
- AddSubmonoid.closurestatement · cited by 224
- Submodule.span_leproof · cited by 164
- LE.le.antisymm'proof · cited by 104
- AddSubmonoid.subset_closureproof · cited by 63
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