[Merged by Bors] - chore(topology/uniform_space/cauchy): add a few simple lemmas #9685
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* rename `cauchy_prod` to `cauchy.prod`; * add `cauchy_seq.tendsto_uniformity`, `cauchy_seq.nonempty`, `cauchy_seq.comp_tendsto`, `cauchy_seq.prod`, `cauchy_seq.prod_map`, `uniform_continuous.comp_cauchy_seq`, and `filter.tendsto.subseq_mem_entourage`; * drop `[nonempty _]` assumption in `cauchy_seq.mem_entourage`;
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* rename `cauchy_prod` to `cauchy.prod`; * add `cauchy_seq.tendsto_uniformity`, `cauchy_seq.nonempty`, `cauchy_seq.comp_tendsto`, `cauchy_seq.prod`, `cauchy_seq.prod_map`, `uniform_continuous.comp_cauchy_seq`, and `filter.tendsto.subseq_mem_entourage`; * drop `[nonempty _]` assumption in `cauchy_seq.mem_entourage`.
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cauchy_prodtocauchy.prod;cauchy_seq.tendsto_uniformity,cauchy_seq.nonempty,cauchy_seq.comp_tendsto,cauchy_seq.prod,cauchy_seq.prod_map,uniform_continuous.comp_cauchy_seq, andfilter.tendsto.subseq_mem_entourage;[nonempty _]assumption incauchy_seq.mem_entourage.