[Merged by Bors] - chore(analysis/normed_space/basic): introduce norm_smul_le
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Currently `norm_smul_le x y` is just a special case of `(norm_smul x y).le`; but if in future we generalize `normed_space` to work over normed rings, it will continue to hold where `norm_smul` no longer does. This adjusts downstream proofs to use the weaker lemma too when the stronger one isn't needed. This adds the corresponding `nnnorm` and `dist` and `nndist` lemmas too.
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Currently `norm_smul_le x y` is just a special case of `(norm_smul x y).le`; but if in future we generalize `normed_space` to work over normed rings, it will continue to hold where `norm_smul` no longer does. This adjusts downstream proofs to use the weaker lemma too when the stronger one isn't needed, both so that we have less to fix if/when we make the suggested refactor, and because the new spelling is shorter. This adds the corresponding `nnnorm` and `dist` and `nndist` lemmas too.
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norm_smul_lenorm_smul_le
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Currently
norm_smul_le x yis just a special case of(norm_smul x y).le; but if in future we generalizenormed_spaceto work over normed rings, it will continue to hold wherenorm_smulno longer does. This adjusts downstream proofs to use the weaker lemma too when the stronger one isn't needed, both so that we have less to fix if/when we make the suggested refactor, and because the new spelling is shorter.This adds the corresponding
nnnormanddistandnndistlemmas too.