refactor: golf Analytic/IteratedFDeriv, SpecialFunctions/

Mathlib/Analysis/Analytic/IteratedFDeriv.lean

@@ -127,17 +127,9 @@ lemma ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal
   rw [← sum_comp (Equiv.embeddingEquivOfFinite (Fin n))]
   congr with σ
   congr with i
-  have A : ∃ y, σ y = i := by
-    have : Function.Bijective σ := (Fintype.bijective_iff_injective_and_card _).2 ⟨σ.injective, rfl⟩
-    exact this.surjective i
-  rcases A with ⟨y, rfl⟩
-  simp only [EmbeddingLike.apply_eq_iff_eq, exists_eq, ↓reduceDIte,
-    Function.Embedding.toEquivRange_symm_apply_self, ContinuousLinearMap.coe_pi',
-    ContinuousLinearMap.coe_id', id_eq, g]
-  congr 1
-  symm
+  obtain ⟨y, rfl⟩ := σ.equivOfFiniteSelfEmbedding.surjective i
   simp [inv_apply, Perm.inv_def,
-    ofBijective_symm_apply_apply, Function.Embedding.equivOfFiniteSelfEmbedding]
+    ofBijective_symm_apply_apply, Function.Embedding.equivOfFiniteSelfEmbedding, g]
 
 private lemma HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum_of_subset
     (h : HasFPowerSeriesWithinOnBall f p s x r) (h' : AnalyticOn 𝕜 f s)

Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean

@@ -408,18 +408,8 @@ def Gamma (s : ℝ) : ℝ :=
 set_option backward.isDefEq.respectTransparency false in
 theorem Gamma_eq_integral {s : ℝ} (hs : 0 < s) :
     Gamma s = ∫ x in Ioi 0, exp (-x) * x ^ (s - 1) := by
-  rw [Gamma, Complex.Gamma_eq_integral (by rwa [Complex.ofReal_re] : 0 < Complex.re s)]
-  dsimp only [Complex.GammaIntegral]
-  simp_rw [← Complex.ofReal_one, ← Complex.ofReal_sub]
-  suffices ∫ x : ℝ in Ioi 0, ↑(exp (-x)) * (x : ℂ) ^ ((s - 1 : ℝ) : ℂ) =
-      ∫ x : ℝ in Ioi 0, ((exp (-x) * x ^ (s - 1) : ℝ) : ℂ) by
-    have cc : ∀ r : ℝ, Complex.ofReal r = @RCLike.ofReal ℂ _ r := fun r => rfl
-    conv_lhs => rw [this]; enter [1, 2, x]; rw [cc]
-    rw [_root_.integral_ofReal, ← cc, Complex.ofReal_re]
-  refine setIntegral_congr_fun measurableSet_Ioi fun x hx => ?_
-  push_cast
-  rw [Complex.ofReal_cpow (le_of_lt hx)]
-  push_cast; rfl
+  rw [Gamma, Complex.Gamma_eq_integral (by rwa [Complex.ofReal_re] : 0 < Complex.re s),
+    Complex.GammaIntegral_ofReal, Complex.ofReal_re]
 
 theorem Gamma_add_one {s : ℝ} (hs : s ≠ 0) : Gamma (s + 1) = s * Gamma s := by
   simp_rw [Gamma]

Mathlib/Analysis/SpecialFunctions/Gaussian/FourierTransform.lean

@@ -97,13 +97,7 @@ theorem verticalIntegral_norm_le (hb : 0 < b.re) (c : ℝ) {T : ℝ} (hT : 0 ≤
       rw [mul_assoc]
   · intro y hy
     have absy : |y| ≤ |c| := by
-      rcases le_or_gt 0 c with (h | h)
-      · rw [uIoc_of_le h] at hy
-        rw [abs_of_nonneg h, abs_of_pos hy.1]
-        exact hy.2
-      · rw [uIoc_of_ge h.le] at hy
-        rw [abs_of_neg h, abs_of_nonpos hy.2, neg_le_neg_iff]
-        exact hy.1.le
+      simpa using Set.abs_sub_left_of_mem_uIcc (Set.uIoc_subset_uIcc hy)
     rw [norm_mul, norm_I, one_mul, two_mul]
     refine (norm_sub_le _ _).trans (add_le_add (vert_norm_bound hT absy) ?_)
     rw [← abs_neg y] at absy