diff --git a/Mathlib/Analysis/Complex/Basic.lean b/Mathlib/Analysis/Complex/Basic.lean index f9e2635ce44ec..58b033e8e1ded 100644 --- a/Mathlib/Analysis/Complex/Basic.lean +++ b/Mathlib/Analysis/Complex/Basic.lean @@ -171,7 +171,7 @@ theorem norm_nat (n : ℕ) : ‖(n : ℂ)‖ = n := #align complex.norm_nat Complex.norm_nat @[simp 1100] -theorem norm_int {n : ℤ} : ‖(n : ℂ)‖ = |(n : ℝ)| := (int_cast_abs n).symm +lemma norm_int {n : ℤ} : ‖(n : ℂ)‖ = |(n : ℝ)| := abs_intCast n #align complex.norm_int Complex.norm_int theorem norm_int_of_nonneg {n : ℤ} (hn : 0 ≤ n) : ‖(n : ℂ)‖ = n := by diff --git a/Mathlib/Data/Complex/Abs.lean b/Mathlib/Data/Complex/Abs.lean index 9020392a408bb..a0e4105602899 100644 --- a/Mathlib/Data/Complex/Abs.lean +++ b/Mathlib/Data/Complex/Abs.lean @@ -237,10 +237,11 @@ theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / Complex.abs z| ≤ 1 := div_le_iff (AbsoluteValue.pos Complex.abs hz), one_mul, abs_im_le_abs] #align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_one -@[simp, norm_cast] -theorem int_cast_abs (n : ℤ) : |↑n| = Complex.abs n := by - rw [← ofReal_int_cast, abs_ofReal] -#align complex.int_cast_abs Complex.int_cast_abs +@[simp, norm_cast] lemma abs_intCast (n : ℤ) : abs n = |↑n| := by rw [← ofReal_int_cast, abs_ofReal] +#align complex.int_cast_abs Complex.abs_intCast + +-- 2024-02-14 +@[deprecated] lemma int_cast_abs (n : ℤ) : |↑n| = Complex.abs n := (abs_intCast _).symm theorem normSq_eq_abs (x : ℂ) : normSq x = (Complex.abs x) ^ 2 := by simp [abs, sq, abs_def, Real.mul_self_sqrt (normSq_nonneg _)]