mathlib
7aebb349 - refactor(ring_theory/polynomial/tower): review APIs (#16678)

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3 years ago
refactor(ring_theory/polynomial/tower): review APIs (#16678) Split from #16412. All of the following lemmas move from namespace `is_scalar_tower` to namespace `polynomial`. Rename `aeval_apply` to `aeval_map_algebra_map` and swap the sides of the equality, remove `aeval_map` which is just the same as `aeval_map_algebra_map`. Rename `algebra_map_aeval` to `aeval_algebra_map_apply` and swap the sides of the equality, rename original `aeval_algebra_map_apply` to `aeval_algebra_map_apply_eq_algebra_map_eval`. Make the new lemma a `simp` lemma and remove `simp` from the original one. Rename `aeval_eq_zero_of_aeval_algebra_map_eq_zero` to `aeval_algebra_map_eq_zero_iff_of_injective` and make it an iff lemma. Replace `aeval_eq_zero_of_aeval_algebra_map_eq_zero_field` by `aeval_algebra_map_eq_zero_iff`, it has weaker assumptions and is also an iff lemma. - [x] depends on: #16673
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