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chore: remove a superfluous by in GroupTheory.Perm.Cycle.Factors (#16465)
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Mathlib/GroupTheory/Perm/Cycle/Factors.lean

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@@ -303,12 +303,10 @@ section cycleFactors
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open scoped List in
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/-- Given a list `l : List α` and a permutation `f : Perm α` whose nonfixed points are all in `l`,
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recursively factors `f` into cycles. -/
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def cycleFactorsAux [DecidableEq α] [Fintype α] :
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∀ (l : List α) (f : Perm α),
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(∀ {x}, f x ≠ x → x ∈ l) →
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{ l : List (Perm α) // l.prod = f ∧ (∀ g ∈ l, IsCycle g) ∧ l.Pairwise Disjoint } := by
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intro l f h
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exact match l with
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def cycleFactorsAux [DecidableEq α] [Fintype α] (l : List α) (f : Perm α)
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(h : ∀ {x}, f x ≠ x → x ∈ l) :
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{ l : List (Perm α) // l.prod = f ∧ (∀ g ∈ l, IsCycle g) ∧ l.Pairwise Disjoint } :=
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match l with
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| [] => ⟨[], by
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{ simp only [imp_false, List.Pairwise.nil, List.not_mem_nil, forall_const, and_true_iff,
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forall_prop_of_false, Classical.not_not, not_false_iff, List.prod_nil] at *

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