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feat(Algebra/FreeMonoid): FreeMonoid.length is surjective #41928

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feat(Algebra/FreeMonoid): FreeMonoid.length is surjective #41928

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4 changes: 4 additions & 0 deletions Mathlib/Algebra/FreeMonoid/Basic.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -172,6 +172,10 @@ theorem length_eq_zero : length a = 0 ↔ a = 1 := List.length_eq_zero_iff
@[to_additive (attr := simp)]
theorem length_of (m : α) : length (of m) = 1 := rfl

@[to_additive]
theorem length_surjective [hα : Nonempty α] : (@length α).Surjective :=
hα.elim fun a n => ⟨FreeMonoid.ofList (List.replicate n a), by simp [length]⟩

@[to_additive FreeAddMonoid.length_eq_one]
theorem length_eq_one : length a = 1 ↔ ∃ m, a = FreeMonoid.of m :=
List.length_eq_one_iff
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