[Merged by Bors] - chore(analysis/normed_space): define norm_one_class
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Many normed rings have `∥1⊫1`. Add a typeclass mixin for this property.
robertylewis
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Sep 30, 2020
hrmacbeth
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Sep 30, 2020
This can't be an instance because Lean can't guess |
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LGTM. Since @PatrickMassot was pinged earlier, let's leave it open til he wakes up. |
hrmacbeth
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Oct 1, 2020
urkud
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Oct 1, 2020
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bors merge |
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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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norm_one_classnorm_one_class
adomani
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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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Many normed rings have
∥1⊫1. Add a typeclass mixin for this property.API changes:
normed_field.norm_one, usenorm_oneinstead;normed_field.nnnorm_one;norm_one_classfor∥1∥ = 1;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
listor afinsetis nonempty, while the other versionsassume
[norm_one_class];norm_pow_letonorm_pow_le', newnorm_pow_leassumes[norm_one_class]insteadof
0 < n;lists andfinsets.