[Merged by Bors] - chore(algebra/algebra/subalgebra): Add missing coe_sort for subalgebra #6800
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semorrison
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src/algebra/algebra/subalgebra.lean
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| instance : has_coe (subalgebra R A) (subsemiring A) := | ||
| ⟨λ S, { ..S }⟩ | ||
| instance : has_coe_t (subalgebra R A) (set A) := ⟨λ s, s.carrier⟩ | ||
| instance : has_mem A (subalgebra R A) := ⟨λ x p, x ∈ (p : set A)⟩ | ||
| instance : has_coe_to_sort (subalgebra R A) := ⟨_, λ p, {x : A // x ∈ p}⟩ |
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Can we add a comment here, explaining why we don't want to define coercions to submodule and subsemiring?
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The main reason is just "none of the other objects do it, and it creates more API that we have to write"
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#6800) Unlike all the other subobject types, `subalgebra` does not implement `has_coe_to_sort` directly, instead going via a coercion to one of `submodule` and `subsemiring`. This removes the `has_coe (subalgebra R A) (subsemiring A)` and `has_coe (subalgebra R A) (submodule R A)` instances; we don't have these for any other subobjects, and they cause the elaborator more difficulty than the corresponding `to_subsemiring` and `to_submodule` projections. This changes the definition of `le` to not involve coercions, which matches `submodule` but requires a few proofs to change. This speeds up the `lift_of_splits` proof by adding `finite_dimensional.of_subalgebra_to_submodule`.
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#6800) Unlike all the other subobject types, `subalgebra` does not implement `has_coe_to_sort` directly, instead going via a coercion to one of `submodule` and `subsemiring`. This removes the `has_coe (subalgebra R A) (subsemiring A)` and `has_coe (subalgebra R A) (submodule R A)` instances; we don't have these for any other subobjects, and they cause the elaborator more difficulty than the corresponding `to_subsemiring` and `to_submodule` projections. This changes the definition of `le` to not involve coercions, which matches `submodule` but requires a few proofs to change. This speeds up the `lift_of_splits` proof by adding `finite_dimensional.of_subalgebra_to_submodule`.
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Unlike all the other subobject types,
subalgebradoes not implementhas_coe_to_sortdirectly, instead going via a coercion to one ofsubmoduleandsubsemiring.This removes the
has_coe (subalgebra R A) (subsemiring A)andhas_coe (subalgebra R A) (submodule R A)instances; we don't have these for any other subobjects, and they cause the elaborator more difficulty than the correspondingto_subsemiringandto_submoduleprojections.This changes the definition of
leto not involve coercions, which matchessubmodulebut requires a few proofs to change.This speeds up the
lift_of_splitsproof by addingfinite_dimensional.of_subalgebra_to_submodule.Split from #6768.