[Merged by Bors] - feat(LiminfLimsup, LpSeminorm): add lemmas/golf #8300
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Co-authored-by: Rémy Degenne <remydegenne@gmail.com>
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- Add `blimsup_eq_limsup` and `bliminf_eq_liminf` - Generalize `limsup_nat_add` and `liminf_nat_add` to a `ConditionallyCompleteLattice`. - Add `Filter.HasBasis.blimsup_eq_iInf_iSup`. - Add `limsup_sup_filter`, `liminf_sup_filter`, `blimsup_sup_not`, `bliminf_inf_not`, `blimsup_not_sup`, `bliminf_not_inf`, `limsup_piecewise`, and `liminf_piecewise`. - Add `essSup_piecewise`. - Assume that the codomain is `ℝ≥0∞` in `essSup_indicator_eq_essSup_restrict`. This allows us to drop assumptions `0 ≤ᵐ[_] f` and `μ s ≠ 0`. - Upgrade inequality to an equality in `snormEssSup_piecewise_le` (now `snormEssSup_piecewise`) and `snorm_top_piecewise_le` (now `snorm_top_piecewise`). - Use new lemmas to golf some proofs.
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- Add `blimsup_eq_limsup` and `bliminf_eq_liminf` - Generalize `limsup_nat_add` and `liminf_nat_add` to a `ConditionallyCompleteLattice`. - Add `Filter.HasBasis.blimsup_eq_iInf_iSup`. - Add `limsup_sup_filter`, `liminf_sup_filter`, `blimsup_sup_not`, `bliminf_inf_not`, `blimsup_not_sup`, `bliminf_not_inf`, `limsup_piecewise`, and `liminf_piecewise`. - Add `essSup_piecewise`. - Assume that the codomain is `ℝ≥0∞` in `essSup_indicator_eq_essSup_restrict`. This allows us to drop assumptions `0 ≤ᵐ[_] f` and `μ s ≠ 0`. - Upgrade inequality to an equality in `snormEssSup_piecewise_le` (now `snormEssSup_piecewise`) and `snorm_top_piecewise_le` (now `snorm_top_piecewise`). - Use new lemmas to golf some proofs.
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blimsup_eq_limsupandbliminf_eq_liminflimsup_nat_addandliminf_nat_addto a
ConditionallyCompleteLattice.Filter.HasBasis.blimsup_eq_iInf_iSup.limsup_sup_filter,liminf_sup_filter,blimsup_sup_not,bliminf_inf_not,blimsup_not_sup,bliminf_not_inf,limsup_piecewise, andliminf_piecewise.essSup_piecewise.ℝ≥0∞in
essSup_indicator_eq_essSup_restrict.This allows us to drop assumptions
0 ≤ᵐ[_] fandμ s ≠ 0.snormEssSup_piecewise_le(nowsnormEssSup_piecewise) andsnorm_top_piecewise_le(nowsnorm_top_piecewise).