mathlib
48518578 - chore(analysis/normed_space): define `norm_one_class` (#4323)

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5 years ago
chore(analysis/normed_space): define `norm_one_class` (#4323) Many normed rings have `∥1⊫1`. Add a typeclass mixin for this property. API changes: * drop `normed_field.norm_one`, use `norm_one` instead; * same with `normed_field.nnnorm_one`; * new typeclass `norm_one_class` for `∥1∥ = 1`; * add `list.norm_prod_le`, `list.norm_prod_le`, `finset.norm_prod_le`, `finset.norm_prod_le'`: norm of the product of finitely many elements is less than or equal to the product of their norms; versions with prime assume that a `list` or a `finset` is nonempty, while the other versions assume `[norm_one_class]`; * rename `norm_pow_le` to `norm_pow_le'`, new `norm_pow_le` assumes `[norm_one_class]` instead of `0 < n`; * add a few supporting lemmas about `list`s and `finset`s.
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