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chore(data/polynomial/field_division): beta-reduce (#10835)
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gebner committed Dec 16, 2021
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2 changes: 1 addition & 1 deletion src/data/polynomial/field_division.lean
Expand Up @@ -429,7 +429,7 @@ end

lemma prod_multiset_root_eq_finset_root (p : polynomial R) :
(multiset.map (λ (a : R), X - C a) p.roots).prod =
∏ a in (multiset.to_finset p.roots), (λ (a : R), (X - C a) ^ (root_multiplicity a p)) a :=
∏ a in p.roots.to_finset, (X - C a) ^ root_multiplicity a p :=
by simp only [count_roots, finset.prod_multiset_map_count]

/-- The product `∏ (X - a)` for `a` inside the multiset `p.roots` divides `p`. -/
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