[Merged by Bors] - refactor(linear_algebra/finsupp): replace mem_span_iff_total #7735
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Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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This PR renames the existing `mem_span_iff_total` to `mem_span_image_iff_total` and the existing `span_eq_map_total` to `span_image_eq_map_total`, and replaces them with slightly simpler lemmas about sets in the module, rather than indexed families. As usual in the linear algebra library, there is tension between using sets and using indexed families, but as `span` is defined in terms of sets I think the new lemmas merit taking the simpler names. Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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This PR renames the existing
mem_span_iff_totaltomem_span_image_iff_totaland the existingspan_eq_map_totaltospan_image_eq_map_total, and replaces them with slightly simpler lemmas about sets in the module, rather than indexed families.As usual in the linear algebra library, there is tension between using sets and using indexed families, but as
spanis defined in terms of sets I think the new lemmas merit taking the simpler names.