@@ -1218,33 +1218,29 @@ open Multiplicative
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-- Porting note: the proof became a little roundabout while porting.
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@[simp]
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- theorem Nat.to_add_pow (a : Multiplicative ℕ) (b : ℕ) : toAdd (a ^ b) = toAdd a * b := by
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- induction' b with b ihs
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- · erw [_root_.pow_zero, toAdd_one, mul_zero]
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- · simp [*, _root_.pow_succ, add_comm, Nat.mul_succ]
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- #align nat.to_add_pow Nat.to_add_pow
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+ theorem Nat.toAdd_pow (a : Multiplicative ℕ) (b : ℕ) : toAdd (a ^ b) = toAdd a * b :=
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+ mul_comm _ _
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+ #align nat.to_add_pow Nat.toAdd_pow
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@[simp]
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- theorem Nat.of_add_mul (a b : ℕ) : ofAdd (a * b) = ofAdd a ^ b :=
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- (Nat.to_add_pow _ _).symm
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- #align nat.of_add_mul Nat.of_add_mul
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+ theorem Nat.ofAdd_mul (a b : ℕ) : ofAdd (a * b) = ofAdd a ^ b :=
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+ (Nat.toAdd_pow _ _).symm
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+ #align nat.of_add_mul Nat.ofAdd_mul
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@[simp]
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- theorem Int.to_add_pow (a : Multiplicative ℤ) (b : ℕ) : toAdd (a ^ b) = toAdd a * b := by
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- induction b <;> simp [*, mul_add, pow_succ, add_comm]
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- #align int.to_add_pow Int.to_add_pow
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+ theorem Int.toAdd_pow (a : Multiplicative ℤ) (b : ℕ) : toAdd (a ^ b) = toAdd a * b :=
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+ mul_comm _ _
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+ #align int.to_add_pow Int.toAdd_pow
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@[simp]
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- theorem Int.to_add_zpow (a : Multiplicative ℤ) (b : ℤ) : toAdd (a ^ b) = toAdd a * b :=
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- Int.induction_on b (by simp) (by simp (config := { contextual := true }) [zpow_add, mul_add])
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- (by
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- simp (config := { contextual := true }) [zpow_add, mul_add, sub_eq_add_neg])
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- #align int.to_add_zpow Int.to_add_zpow
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+ theorem Int.toAdd_zpow (a : Multiplicative ℤ) (b : ℤ) : toAdd (a ^ b) = toAdd a * b :=
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+ mul_comm _ _
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+ #align int.to_add_zpow Int.toAdd_zpow
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@[simp]
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- theorem Int.of_add_mul (a b : ℤ) : ofAdd (a * b) = ofAdd a ^ b :=
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- (Int.to_add_zpow _ _).symm
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- #align int.of_add_mul Int.of_add_mul
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+ theorem Int.ofAdd_mul (a b : ℤ) : ofAdd (a * b) = ofAdd a ^ b :=
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+ (Int.toAdd_zpow _ _).symm
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+ #align int.of_add_mul Int.ofAdd_mul
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end Multiplicative
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