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chore(algebra/star/basic): split out
big_operators
import (#17792)
cf #17772 (comment), cc @eric-wieser
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/- | ||
Copyright (c) 2021 Eric Wieser. All rights reserved. | ||
Released under Apache 2.0 license as described in the file LICENSE. | ||
Authors: Eric Wieser | ||
-/ | ||
import algebra.big_operators.basic | ||
import algebra.star.basic | ||
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/-! # Big-operators lemmas about `star` algebraic operations | ||
These results are kept separate from `algebra.star.basic` to avoid it needing to import `finset`. | ||
-/ | ||
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variables {R : Type*} | ||
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open_locale big_operators | ||
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@[simp] lemma star_prod [comm_monoid R] [star_semigroup R] {α : Type*} | ||
(s : finset α) (f : α → R): | ||
star (∏ x in s, f x) = ∏ x in s, star (f x) := | ||
map_prod (star_mul_aut : R ≃* R) _ _ | ||
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@[simp] lemma star_sum [add_comm_monoid R] [star_add_monoid R] {α : Type*} | ||
(s : finset α) (f : α → R): | ||
star (∑ x in s, f x) = ∑ x in s, star (f x) := | ||
(star_add_equiv : R ≃+ R).map_sum _ _ |
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