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chore(algebra/direct_sum/algebra): add missing rfl lemmas (#8924)
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I realized I was resorting to nasty unfolding to get these mid-proof
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eric-wieser committed Aug 30, 2021
1 parent aa0694a commit 4a65197
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6 changes: 6 additions & 0 deletions src/algebra/direct_sum/algebra.lean
Expand Up @@ -88,6 +88,12 @@ instance : algebra R (⨁ i, A i) :=
apply dfinsupp.single_eq_of_sigma_eq (galgebra.smul_def r ⟨i, xi⟩),
end }

lemma algebra_map_apply (r : R) :
algebra_map R (⨁ i, A i) r = direct_sum.of A 0 (galgebra.to_fun r) := rfl

lemma algebra_map_to_add_monoid_hom :
↑(algebra_map R (⨁ i, A i)) = (direct_sum.of A 0).comp (galgebra.to_fun : R →+ A 0) := rfl

section
-- for `simps`
local attribute [simp] linear_map.cod_restrict
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