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fix(GroupTheory/Coprod): fix recursor argument name #41930

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fix(GroupTheory/Coprod): fix recursor argument name #41930

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13 changes: 7 additions & 6 deletions Mathlib/GroupTheory/Coprod/Basic.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -193,10 +193,10 @@ theorem mk_of_inl (x : M) : (mk (of (.inl x)) : M ∗ N) = inl x := rfl
theorem mk_of_inr (x : N) : (mk (of (.inr x)) : M ∗ N) = inr x := rfl

@[to_additive (attr := elab_as_elim)]
theorem induction_on' {C : M ∗ N → Prop} (m : M ∗ N)
(one : C 1)
(inl_mul : ∀ m x, C x → C (inl m * x))
(inr_mul : ∀ n x, C x → C (inr n * x)) : C m := by
theorem induction_on' {motive : M ∗ N → Prop} (m : M ∗ N)
(one : motive 1)
(inl_mul : ∀ m x, motive x → motive (inl m * x))
(inr_mul : ∀ n x, motive x → motive (inr n * x)) : motive m := by
rcases mk_surjective m with ⟨x, rfl⟩
induction x using FreeMonoid.inductionOn' with
| one => exact one
Expand All @@ -206,8 +206,9 @@ theorem induction_on' {C : M ∗ N → Prop} (m : M ∗ N)
| inr n => simpa using inr_mul n _ ih

@[to_additive (attr := elab_as_elim)]
theorem induction_on {C : M ∗ N → Prop} (m : M ∗ N)
(inl : ∀ m, C (inl m)) (inr : ∀ n, C (inr n)) (mul : ∀ x y, C x → C y → C (x * y)) : C m :=
theorem induction_on {motive : M ∗ N → Prop} (m : M ∗ N)
(inl : ∀ m, motive (inl m)) (inr : ∀ n, motive (inr n))
(mul : ∀ x y, motive x → motive y → motive (x * y)) : motive m :=
induction_on' m (by simpa using inl 1) (fun _ _ ↦ mul _ _ (inl _)) fun _ _ ↦ mul _ _ (inr _)

/-- Lift a monoid homomorphism `FreeMonoid (M ⊕ N) →* P` satisfying additional properties to
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