[Merged by Bors] - refactor(algebra/direct_sum/basic): use the new polymorphic subobject API #14341
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… API This doesn't let us deduplicate the lattice lemmas, but does eliminate the duplicate instances and definitions!
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… API (#14341) This doesn't let us deduplicate the lattice lemmas, but does eliminate the duplicate instances and definitions! This merges: * `direct_sum.add_submonoid_is_internal`, `direct_sum.add_subgroup_is_internal`, `direct_sum.submodule_is_internal` into `direct_sum.is_internal` * `direct_sum.add_submonoid_coe`, `direct_sum.add_subgroup_coe` into `direct_sum.coe_add_monoid_hom` * `direct_sum.add_submonoid_coe_ring_hom`, `direct_sum.add_subgroup_coe_ring_hom` into `direct_sum.coe_ring_hom` * `add_submonoid.gsemiring`, `add_subgroup.gsemiring`, `submodule.gsemiring` into `set_like.gsemiring` * `add_submonoid.gcomm_semiring`, `add_subgroup.gcomm_semiring`, `submodule.gcomm_semiring` into `set_like.gcomm_semiring` Renames * `direct_sum.submodule_coe` into `direct_sum.coe_linear_map` * `direct_sum.submodule_coe_alg_hom` into `direct_sum.coe_alg_hom And adds: * `set_like.gnon_unital_non_assoc_semiring`, now that it doesn't need to be repeated three times! A large number of related lemmas are also renamed to match the new definition names. This was what originally motivated the `set_like` typeclass; thanks to @Vierkantor for doing the subobject follow up I never got around to!
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This doesn't let us deduplicate the lattice lemmas, but does eliminate the duplicate instances and definitions!
This merges:
direct_sum.add_submonoid_is_internal,direct_sum.add_subgroup_is_internal,direct_sum.submodule_is_internalintodirect_sum.is_internaldirect_sum.add_submonoid_coe,direct_sum.add_subgroup_coeintodirect_sum.coe_add_monoid_homdirect_sum.add_submonoid_coe_ring_hom,direct_sum.add_subgroup_coe_ring_homintodirect_sum.coe_ring_homadd_submonoid.gsemiring,add_subgroup.gsemiring,submodule.gsemiringintoset_like.gsemiringadd_submonoid.gcomm_semiring,add_subgroup.gcomm_semiring,submodule.gcomm_semiringintoset_like.gcomm_semiringRenames
direct_sum.submodule_coeintodirect_sum.coe_linear_mapdirect_sum.submodule_coe_alg_hominto `direct_sum.coe_alg_homAnd adds:
set_like.gnon_unital_non_assoc_semiring, now that it doesn't need to be repeated three times!A large number of related lemmas are also renamed to match the new definition names.
This was what originally motivated the
set_liketypeclass; thanks to @Vierkantor for doing the subobject follow up I never got around to!