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[Merged by Bors] - feat(topology/continuous_function/algebra): generalize algebra instances#12055
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[Merged by Bors] - feat(topology/continuous_function/algebra): generalize algebra instances#12055eric-wieser wants to merge 16 commits intomasterfrom
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This adds some missing instances in the algebra hierarchy, as well as more fine-grained scalar instances. This also introduces continuity lemmas about `zpow` on groups, which are used to avoid diamonds in the int-action.
eric-wieser
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Feb 15, 2022
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| lemma coe_inj ⦃f g : C(α, β)⦄ (h : (f : α → β) = g) : f = g := | ||
| by cases f; cases g; cases h; refl | ||
| lemma coe_injective : @function.injective (C(α, β)) (α → β) coe_fn := | ||
| λ f g h, by cases f; cases g; congr' |
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I know this should use fun_like, but I didn't want to do too many refactors at the same time.
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…2072) `continuous_linear_map.continuous_nsmul` is nothing to do with `continuous_linear_map`s, and is the same as `continuous_nsmul`, but the latter doesn't require commutativity. There is no reason to keep the former. This lemma was added in #7084, but probably got missed due to how large that PR had to be. We can't remove `continuous_linear_map.continuous_zsmul` until #12055 is merged, as there is currently no `continuous_zsmul` in the root namespace.
urkud
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Feb 16, 2022
urkud
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urkud
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Otherwise LGTM. Thanks! |
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✌️ eric-wieser can now approve this pull request. To approve and merge a pull request, simply reply with |
Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
eric-wieser
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Feb 16, 2022
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…ces (#12055) This adds: * some missing instances in the algebra hierarchy (`comm_semigroup`, `mul_one_class`, `mul_zero_class`, `monoid_with_zero`, `comm_monoid_with_zero`, `comm_semiring`). * finer-grained scalar action instances, notably none of which require `topological_space R` any more, as they only need `has_continuous_const_smul R M` instead of `has_continuous_smul R M`. * continuity lemmas about `zpow` on groups and `zsmul` on additive groups (copied directly from the lemmas about `pow` on monoids), which are used to avoid diamonds in the int-action. In order to make room for these, the lemmas about `zpow` on groups with zero have been renamed to `zpow₀`, which is consistent with how the similar clash with `inv` is solved. * a few lemmas about `mk_of_compact` since an existing proof was broken by `refl` closing the goal earlier than before.
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This adds:
comm_semigroup,mul_one_class,mul_zero_class,monoid_with_zero,comm_monoid_with_zero,comm_semiring).topological_space Rany more, as they only needhas_continuous_const_smul R Minstead ofhas_continuous_smul R M.zpowon groups andzsmulon additive groups (copied directly from the lemmas aboutpowon monoids), which are used to avoid diamonds in the int-action. In order to make room for these, the lemmas aboutzpowon groups with zero have been renamed tozpow₀, which is consistent with how the similar clash withinvis solved.mk_of_compactsince an existing proof was broken byreflclosing the goal earlier than before.