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doc(group_theory/coset): Mention "Lagrange's theorem" (#12137)
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tb65536 and tb65536 committed Feb 19, 2022
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2 changes: 1 addition & 1 deletion src/group_theory/coset.lean
Expand Up @@ -421,7 +421,7 @@ def quotient_subgroup_of_embedding_of_le (H : subgroup α) {K L : subgroup α} (
by rw ← fintype.card_prod;
exact fintype.card_congr (subgroup.group_equiv_quotient_times_subgroup)

/-- **Order of a Subgroup** -/
/-- **Lagrange's Theorem**: The order of a subgroup divides the order of its ambient group. -/
@[to_additive] lemma card_subgroup_dvd_card [fintype α] (s : subgroup α) [fintype s] :
fintype.card s ∣ fintype.card α :=
by classical; simp [card_eq_card_quotient_mul_card_subgroup s, @dvd_mul_left ℕ]
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