[Merged by Bors] - feat(analysis/asymptotics/asymptotics): generalize, golf #15010
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| @@ -143,10 +143,14 @@ theorem is_o.is_O (hgf : f =o[l] g) : f =O[l] g := hgf.is_O_with.is_O | |||
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| lemma is_O.is_O_with : f =O[l] g → ∃ c : ℝ, is_O_with c l f g := is_O_iff_is_O_with.1 | |||
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| theorem is_O_with.weaken' (h : is_O_with c l f g) (hg : ∀ᶠ x in l, 0 ≤ ∥g x∥) (hc : c ≤ c') : | |||
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I don't understand the point of stating things assuming only has_norm and assumptions saying some norms are non negative.
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I left one result of this kind and renamed it to *_aux. It is used to prove two versions of a lemma assuming has_norm/semi_normed_group for different types.
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* add `is_o_iff_nat_mul_le`, `is_o_iff_nat_mul_le'`, `is_o_irrefl`, `is_O.not_is_o`, `is_o.not_is_O`; * generalize lemmas about `1 = o(f)`, `1 = O(f)`, `f = o(1)`, `f = O(1)` to `[has_one F] [norm_one_class F]`, add some `@[simp]` attrs; * rename `is_O_one_of_tendsto` to `filter.tendsto.is_O_one`; * golf some proofs
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* add `is_o_iff_nat_mul_le`, `is_o_iff_nat_mul_le'`, `is_o_irrefl`, `is_O.not_is_o`, `is_o.not_is_O`; * generalize lemmas about `1 = o(f)`, `1 = O(f)`, `f = o(1)`, `f = O(1)` to `[has_one F] [norm_one_class F]`, add some `@[simp]` attrs; * rename `is_O_one_of_tendsto` to `filter.tendsto.is_O_one`; * golf some proofs
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is_o_iff_nat_mul_le,is_o_iff_nat_mul_le',is_o_irrefl,is_O.not_is_o,is_o.not_is_O;1 = o(f),1 = O(f),f = o(1),f = O(1)to[has_one F] [norm_one_class F], add some@[simp]attrs;is_O_one_of_tendstotofilter.tendsto.is_O_one;@[simp]to `real.norm_eq_abs #15006