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chore(algebra/algebra/basic): remove a duplicate instance (#9320)
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`algebra.linear_map.module'` is just a special case of `linear_map.module'`.

`by apply_instance` finds this instance provided it's used after the definition of `is_scalar_tower.to_smul_comm_class`.
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eric-wieser committed Sep 21, 2021
1 parent 420f11a commit 56a6ed6
Showing 1 changed file with 0 additions and 11 deletions.
11 changes: 0 additions & 11 deletions src/algebra/algebra/basic.lean
Expand Up @@ -1341,17 +1341,6 @@ linear_map.coe_injective $ ((lmul_right R a).coe_pow n).symm ▸ (mul_right_iter
@[simp] lemma lmul'_apply {x y : A} : lmul' R (x ⊗ₜ y) = x * y :=
by simp only [algebra.lmul', tensor_product.lift.tmul, alg_hom.to_linear_map_apply, lmul_apply]

instance linear_map.module' (R : Type u) [comm_semiring R]
(M : Type v) [add_comm_monoid M] [module R M]
(S : Type w) [comm_semiring S] [algebra R S] : module S (M →ₗ[R] S) :=
{ smul := λ s f, linear_map.llcomp _ _ _ _ (algebra.lmul R S s) f,
one_smul := λ f, linear_map.ext $ λ x, one_mul _,
mul_smul := λ s₁ s₂ f, linear_map.ext $ λ x, mul_assoc _ _ _,
smul_add := λ s f g, linear_map.map_add _ _ _,
smul_zero := λ s, linear_map.map_zero _,
add_smul := λ s₁ s₂ f, linear_map.ext $ λ x, add_mul _ _ _,
zero_smul := λ f, linear_map.ext $ λ x, zero_mul _ }

end algebra

section ring
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