mathlib3
354fda08 - feat(linear_algebra/finsupp): add mem_span_set (#6457)

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5 years ago
feat(linear_algebra/finsupp): add mem_span_set (#6457) From the doc-string: If `m ∈ M` is contained in the `R`-submodule spanned by a set `s ⊆ M`, then we can write `m` as a finite `R`-linear combination of elements of `s`. The implementation uses `finsupp.sum`. The initial proof was a substantial simplification of mine, due to Kevin Buzzard. The final one is due to Eric Wieser. Zulip discussion for the proof: https://leanprover.zulipchat.com/#narrow/stream/113489-new-members/topic/submodule.2Espan.20as_sum Zulip discussion for the universe issue: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/universe.20issue.20with.20.60Type*.60
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