[Merged by Bors] - chore(topology/instances/ennreal): drop a dependency #18562
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Drop dependency on `analysis.normed.group.basic` by using `nnabs` instead of `nnnorm`.
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Drop dependency on `analysis.normed.group.basic` by using `nnabs` instead of `nnnorm`.
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API changes: * Add `HasSum.sum_range_add`, `sum_add_tsum_nat_add'`, and `tsum_eq_zero_add'`. We had these (or stronger) results for topological groups. These versions works for monoids. * Rename `tendsto_atTop_csupr` to `tendsto_atTop_csupᵢ`, `tendsto_atBot_csupr` to `tendsto_atBot_csupᵢ`, `tendsto_atBot_cinfi` to `tendsto_atBot_cinfᵢ`, and `tendsto_atTop_cinfi` to `tendsto_atTop_cinfᵢ`. * Add a shortcut instance for `T5Space ENNReal`. * Add `ENNReal.nhdsWithin_Ioi_one_neBot`, `ENNReal.nhdsWithin_Ioi_nat_neBot`, `ENNReal.nhdsWithin_Ioi_ofNat_nebot`, and `ENNReal.nhdsWithin_Iio_neBot`. * Add `ENNReal.hasBasis_nhds_of_ne_top` and `ENNReal.hasBasis_nhds_of_ne_top'`. * Add `ENNReal.binfᵢ_le_nhds` and `ENNReal.tendsto_nhds_of_Icc`. * Use `Real.nnabs` instead of `nnnorm` to avoid dependency on `analysis.normed.group.basic` (forward-port of leanprover-community/mathlib#18562). * Add `ENNReal.tsum_eq_limsup_sum_nat`. * Add `ENNReal.tsum_comp_le_tsum_of_injective`, `ENNReal.tsum_le_tsum_comp_of_surjective`, use them to golf some proofs. * Add `ENNReal.tsum_bunionᵢ_le_tsum`, `ENNReal.tsum_unionᵢ_le_tsum`. We had versions of these lemmas for finite collections. The proofs for infinite collections are simpler. Most of these changes were done to fix some long proofs: it was easier for me (@urkud) to add supporting lemmas and golf the proof than to fix the original code. Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Yury Kudryashov <urkud@urkud.name>
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Drop dependency on
analysis.normed.group.basicby usingnnabsinstead ofnnnorm.