chore: golf a bit

HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/ToSols.lean

@@ -286,11 +286,8 @@ lemma inLineEqToSol_proj (T : InLineEqSol) : inLineEqToSol (inLineEqProj T) = T.
 /-- Given an element of `inQuad × ℚ × ℚ × ℚ`, a solution to the ACCs. -/
 def inQuadToSol : InQuad × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R, a₁, a₂, a₃) =>
   AnomalyFreeMk' (lineCube R.val.val a₁ a₂ a₃)
-    (by
-      erw [planeY₃B₃_quad]
-      rw [R.prop.1, R.prop.2.1, R.prop.2.2]
-      simp)
-    (lineCube_cube R.val.val a₁ a₂ a₃)
+    (by erw [planeY₃B₃_quad, R.prop.1, R.prop.2.1, R.prop.2.2]; simp)
+      (lineCube_cube R.val.val a₁ a₂ a₃)
 
 lemma inQuadToSol_smul (R : InQuad) (c₁ c₂ c₃ d : ℚ) :
     inQuadToSol (R, (d * c₁), (d * c₂), (d * c₃)) = d • inQuadToSol (R, c₁, c₂, c₃) := by
@@ -314,9 +311,7 @@ lemma inQuadToSol_proj (T : InQuadSol) : inQuadToSol (inQuadProj T) = T.val := b
   rw [inQuadProj, inQuadToSol_smul]
   apply ACCSystem.Sols.ext
   change _ • (planeY₃B₃ _ _ _ _).val = _
-  rw [planeY₃B₃_val]
-  rw [Y₃_plus_B₃_plus_proj]
-  rw [cube_proj, cube_proj_proj_B₃, cube_proj_proj_Y₃]
+  rw [planeY₃B₃_val, Y₃_plus_B₃_plus_proj, cube_proj, cube_proj_proj_B₃, cube_proj_proj_Y₃]
   ring_nf
   simp only [zero_smul, add_zero, Fin.isValue, Fin.reduceFinMk, zero_add]
   have h1 : (cubeTriLin T.val.val T.val.val Y₃.val ^ 2 * dot Y₃.val B₃.val ^ 3 * 3 +
@@ -331,14 +326,8 @@ lemma inQuadToSol_proj (T : InQuadSol) : inQuadToSol (inQuadProj T) = T.val := b
 /-- Given a element of `inQuadCube × ℚ × ℚ × ℚ`, a solution to the ACCs. -/
 def inQuadCubeToSol : InQuadCube × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R, b₁, b₂, b₃) =>
   AnomalyFreeMk' (planeY₃B₃ R.val.val.val b₁ b₂ b₃)
-  (by
-    rw [planeY₃B₃_quad]
-    rw [R.val.prop.1, R.val.prop.2.1, R.val.prop.2.2]
-    simp)
-  (by
-    rw [planeY₃B₃_cubic]
-    rw [R.prop.1, R.prop.2.1, R.prop.2.2]
-    simp)
+  (by rw [planeY₃B₃_quad, R.val.prop.1, R.val.prop.2.1, R.val.prop.2.2]; simp)
+  (by rw [planeY₃B₃_cubic, R.prop.1, R.prop.2.1, R.prop.2.2]; simp)
 
 lemma inQuadCubeToSol_smul (R : InQuadCube) (c₁ c₂ c₃ d : ℚ) :
     inQuadCubeToSol (R, (d * c₁), (d * c₂), (d * c₃)) = d • inQuadCubeToSol (R, c₁, c₂, c₃) := by
@@ -361,8 +350,7 @@ lemma inQuadCubeToSol_proj (T : InQuadCubeSol) :
   rw [inQuadCubeProj, inQuadCubeToSol_smul]
   apply ACCSystem.Sols.ext
   change _ • (planeY₃B₃ _ _ _ _).val = _
-  rw [planeY₃B₃_val]
-  rw [Y₃_plus_B₃_plus_proj]
+  rw [planeY₃B₃_val, Y₃_plus_B₃_plus_proj]
   ring_nf
   simp only [Fin.isValue, Fin.reduceFinMk, zero_smul, add_zero, zero_add]
   rw [← MulAction.mul_smul, mul_comm, mul_inv_cancel₀]
@@ -389,17 +377,15 @@ lemma toSol_toSolNSProj (T : NotInLineEqSol) :
   use toSolNSProj T.val
   have h1 : ¬ LineEqProp (toSolNSProj T.val).1 :=
     (linEqPropSol_iff_proj_linEqProp T.val).mpr.mt T.prop
-  rw [toSol]
-  simp_all
+  simp_rw [toSol, h1]
   exact toSolNS_proj T
 
 lemma toSol_inLineEq (T : InLineEqSol) : ∃ X, toSol X = T.val := by
   let X := inLineEqProj T
   use ⟨X.1.val, X.2.1, X.2.2⟩
   have : ¬ InQuadProp X.1.val := (inQuadSolProp_iff_proj_inQuadProp T.val).mpr.mt T.prop.2
   have : LineEqProp X.1.val := (linEqPropSol_iff_proj_linEqProp T.val).mp T.prop.1
-  rw [toSol]
-  simp_all
+  simp_all only [toSol]
   exact inLineEqToSol_proj T
 
 lemma toSol_inQuad (T : InQuadSol) : ∃ X, toSol X = T.val := by
@@ -408,8 +394,7 @@ lemma toSol_inQuad (T : InQuadSol) : ∃ X, toSol X = T.val := by
   have : ¬ InCubeProp X.1.val.val := (inCubeSolProp_iff_proj_inCubeProp T.val).mpr.mt T.prop.2.2
   have : InQuadProp X.1.val.val := (inQuadSolProp_iff_proj_inQuadProp T.val).mp T.prop.2.1
   have : LineEqProp X.1.val.val := (linEqPropSol_iff_proj_linEqProp T.val).mp T.prop.1
-  rw [toSol]
-  simp_all
+  simp_all only [toSol]
   exact inQuadToSol_proj T
 
 lemma toSol_inQuadCube (T : InQuadCubeSol) : ∃ X, toSol X = T.val := by
@@ -418,8 +403,7 @@ lemma toSol_inQuadCube (T : InQuadCubeSol) : ∃ X, toSol X = T.val := by
   have : InCubeProp X.1.val.val.val := (inCubeSolProp_iff_proj_inCubeProp T.val).mp T.prop.2.2
   have : InQuadProp X.1.val.val.val := (inQuadSolProp_iff_proj_inQuadProp T.val).mp T.prop.2.1
   have : LineEqProp X.1.val.val.val := (linEqPropSol_iff_proj_linEqProp T.val).mp T.prop.1
-  rw [toSol]
-  simp_all
+  simp_all only [toSol]
   exact inQuadCubeToSol_proj T
 
 theorem toSol_surjective : Function.Surjective toSol := by

HepLean/AnomalyCancellation/PureU1/Even/LineInCubic.lean

@@ -136,7 +136,7 @@ lemma lineInCubicPerm_last_cond {S : (PureU1 (2 * n.succ.succ)).LinSols}
   rw [P_P_P!_accCube' g f hfg] at h1
   simp only [Nat.succ_eq_add_one, neg_add_rev, mul_eq_zero] at h1
   cases h1 <;> rename_i h1
-  · apply Or.inl
+  · left
     linear_combination h1
   · cases h1 <;> rename_i h1
     · refine Or.inr (Or.inl ?_)

HepLean/AnomalyCancellation/PureU1/Odd/LineInCubic.lean

@@ -123,7 +123,7 @@ lemma lineInCubicPerm_last_cond {S : (PureU1 (2 * n.succ.succ+1)).LinSols}
   rw [P_P_P!_accCube' g f hfg] at h1
   simp only [Nat.succ_eq_add_one, mul_eq_zero] at h1
   cases h1 <;> rename_i h1
-  · apply Or.inl
+  · left
     linear_combination h1
   · cases h1 <;> rename_i h1
     · refine Or.inr (Or.inl ?_)

HepLean/BeyondTheStandardModel/TwoHDM/Basic.lean

@@ -75,7 +75,7 @@ lemma swap_fields : P.toFun Φ1 Φ2 =
     normSq_apply_im_zero, mul_zero, zero_add, RingHomCompTriple.comp_apply, RingHom.id_apply]
   ring_nf
   simp only [one_div, add_left_inj, add_right_inj, mul_eq_mul_left_iff]
-  apply Or.inl
+  left
   rw [HiggsField.innerProd, HiggsField.innerProd, ← InnerProductSpace.conj_symm, Complex.abs_conj]
 
 /-- If `Φ₂` is zero the potential reduces to the Higgs potential on `Φ₁`. -/

HepLean/FlavorPhysics/CKMMatrix/StandardParameterization/StandardParameters.lean

@@ -69,8 +69,7 @@ section sines
 /-- For a CKM matrix `sin θ₁₂` is non-negative. -/
 lemma S₁₂_nonneg (V : Quotient CKMMatrixSetoid) : 0 ≤ S₁₂ V := by
   rw [S₁₂, div_nonneg_iff]
-  apply Or.inl
-  apply (And.intro (VAbs_ge_zero 0 1 V) (Real.sqrt_nonneg (VudAbs V ^ 2 + VusAbs V ^ 2)))
+  exact .inl (.intro (VAbs_ge_zero 0 1 V) (Real.sqrt_nonneg (VudAbs V ^ 2 + VusAbs V ^ 2)))
 
 /-- For a CKM matrix `sin θ₁₃` is non-negative. -/
 lemma S₁₃_nonneg (V : Quotient CKMMatrixSetoid) : 0 ≤ S₁₃ V :=
@@ -82,8 +81,7 @@ lemma S₂₃_nonneg (V : Quotient CKMMatrixSetoid) : 0 ≤ S₂₃ V := by
   · rw [S₂₃, if_pos ha]
     exact VAbs_ge_zero 1 0 V
   · rw [S₂₃, if_neg ha, @div_nonneg_iff]
-    apply Or.inl
-    apply And.intro (VAbs_ge_zero 1 2 V) (Real.sqrt_nonneg (VudAbs V ^ 2 + VusAbs V ^ 2))
+    exact .inl (.intro (VAbs_ge_zero 1 2 V) (Real.sqrt_nonneg (VudAbs V ^ 2 + VusAbs V ^ 2)))
 
 /-- For a CKM matrix `sin θ₁₂` is less then or equal to 1. -/
 lemma S₁₂_leq_one (V : Quotient CKMMatrixSetoid) : S₁₂ V ≤ 1 := by
@@ -95,7 +93,7 @@ lemma S₁₂_leq_one (V : Quotient CKMMatrixSetoid) : S₁₂ V ≤ 1 := by
       cases' h2 with h2 h2
       simp_all
       exact h2
-    apply Or.inl
+    left
     simp_all only [VudAbs, VusAbs, or_true, Real.sqrt_pos, true_and]
     rw [Real.le_sqrt (VAbs_ge_zero 0 1 V) (le_of_lt h3)]
     simp only [Fin.isValue, le_add_iff_nonneg_left]

HepLean/Lorentz/Group/Boosts.lean

@@ -150,7 +150,7 @@ lemma toMatrix_apply (u v : FuturePointing d) (μ ν : Fin 1 ⊕ Fin d) :
     Action.instMonoidalCategory_tensorUnit_V, CategoryTheory.Equivalence.symm_inverse,
     Action.functorCategoryEquivalence_functor, Action.FunctorCategoryEquivalence.functor_obj_obj,
     Pi.smul_apply, smul_eq_mul, Pi.sub_apply, Pi.neg_apply]
-  apply Or.inl
+  left
   ring
 
 open minkowskiMatrix in

HepLean/Mathematics/Fin/Involutions.lean

@@ -208,8 +208,7 @@ def involutionAddEquiv {n : ℕ} (f : {f : Fin n → Fin n // Function.Involutiv
         simp_all only [Subtype.coe_eta] }
   let s : Finset (Fin n) := Finset.univ.filter fun i => f.1 i = i
   let e2' : { i : Fin n // f.1 i = i} ≃ {i // i ∈ s} := by
-    refine Equiv.subtypeEquivProp ?h
-    funext i
+    apply Equiv.subtypeEquivProp
     simp [s]
   let e2 : {i // i ∈ s} ≃ Fin (Finset.card s) := by
     refine (Finset.orderIsoOfFin _ ?_).symm.toEquiv
@@ -242,7 +241,7 @@ lemma involutionAddEquiv_cast {n : ℕ} {f1 f2 : {f : Fin n → Fin n // Functio
     involutionAddEquiv f1 = (Equiv.subtypeEquivRight (by rw [hf]; simp)).trans
       ((involutionAddEquiv f2).trans (Equiv.optionCongr (finCongr (by rw [hf])))) := by
   subst hf
-  simp only [finCongr_refl, Equiv.optionCongr_refl, Equiv.trans_refl]
+  rw [finCongr_refl, Equiv.optionCongr_refl]
   rfl
 
 lemma involutionAddEquiv_cast' {m : ℕ} {f1 f2 : {f : Fin m → Fin m // Function.Involutive f}}
@@ -259,33 +258,18 @@ lemma involutionAddEquiv_none_succ {n : ℕ}
     (h : involutionAddEquiv (involutionCons n f).1 (involutionCons n f).2 = none)
     (x : Fin n) : f.1 x.succ = x.succ ↔ (involutionCons n f).1.1 x = x := by
   simp only [succ_eq_add_one, involutionCons, Fin.cons_update, Equiv.coe_fn_mk, dite_eq_left_iff]
-  have hn' := involutionAddEquiv_none_image_zero h
-  have hx : ¬ f.1 x.succ = ⟨0, Nat.zero_lt_succ n⟩:= by
-    rw [← hn']
-    exact fun hn => Fin.succ_ne_zero x (Function.Involutive.injective f.2 hn)
-  apply Iff.intro
-  · intro h2 h3
-    rw [Fin.ext_iff]
-    simp [h2]
-  · intro h2
-    have h2' := h2 hx
-    conv_rhs => rw [← h2']
-    simp
+  have hx : ¬ f.1 x.succ = ⟨0, Nat.zero_lt_succ n⟩:=
+    involutionAddEquiv_none_image_zero h ▸
+      fun hn => Fin.succ_ne_zero x (Function.Involutive.injective f.2 hn)
+  exact Iff.intro (fun h2 ↦ by simp [h2]) (fun h2 ↦ (Fin.pred_eq_iff_eq_succ hx).mp (h2 hx))
 
 lemma involutionAddEquiv_isSome_image_zero {n : ℕ} :
     {f : {f : Fin n.succ → Fin n.succ // Function.Involutive f}}
     → (involutionAddEquiv (involutionCons n f).1 (involutionCons n f).2).isSome
     → ¬ f.1 ⟨0, Nat.zero_lt_succ n⟩ = ⟨0, Nat.zero_lt_succ n⟩ := by
-  intro f hf
-  simp only [succ_eq_add_one, involutionCons, Equiv.coe_fn_mk, involutionAddEquiv,
-    Option.isSome_some, Option.get_some, Option.isSome_none, Equiv.trans_apply,
-    Equiv.optionCongr_apply, Equiv.coe_trans, RelIso.coe_fn_toEquiv, Option.isSome_map'] at hf
-  simp_all only [List.length_cons, Fin.zero_eta]
-  obtain ⟨val, property⟩ := f
-  simp_all only [List.length_cons]
-  apply Aesop.BuiltinRules.not_intro
-  intro a
-  simp_all only [↓reduceDIte, Option.isSome_none, Bool.false_eq_true]
+  intro f hf a
+  simp only [succ_eq_add_one, involutionCons, Equiv.coe_fn_mk, involutionAddEquiv] at hf
+  simp_all
 
 /-!
 
@@ -303,15 +287,11 @@ def involutionNoFixedEquivSum {n : ℕ} :
     ∧ (∀ i, f i ≠ i) ∧ f 0 = k.succ} where
   toFun f := ⟨(f.1 0).pred (f.2.2 0), ⟨f.1, f.2.1, by simpa using f.2.2⟩⟩
   invFun f := ⟨f.2.1, ⟨f.2.2.1, f.2.2.2.1⟩⟩
-  left_inv f := by
-    rfl
+  left_inv f := rfl
   right_inv f := by
-    simp only [succ_eq_add_one, ne_eq, mul_eq]
     ext
-    · simp only [Fin.coe_pred]
-      rw [f.2.2.2.2]
-      simp
-    · simp
+    · simp [f.2.2.2.2]
+    · rfl
 
 /-- The condition on fixed point free involutions of `Fin n.succ` for a fixed value of `f 0`,
   can be modified by conjugation with an equivalence. -/
@@ -329,8 +309,7 @@ def involutionNoFixedZeroSetEquivEquiv {n : ℕ}
     intro i
     simp only [succ_eq_add_one, Function.comp_apply, ne_eq, Equiv.apply_symm_apply]
     have hf2 := f.2.1 i
-    simpa using hf2, by
-      simpa using f.2.2.1, by simpa using f.2.2.2⟩
+    simpa using hf2, by simpa using f.2.2.1, by simpa using f.2.2.2⟩
   left_inv f := by
     ext i
     simp
@@ -485,7 +464,7 @@ def involutionNoFixedSetOne {n : ℕ} :
           simp [Fin.ext_iff] at h
       | ⟨(Nat.succ (Nat.succ m)), h⟩ =>
         simp only [succ_eq_add_one, ne_eq, Fin.ext_iff, Fin.val_succ, add_left_inj, f']
-        have hf:= f.2.2 ⟨m, by exact Nat.add_lt_add_iff_right.mp h⟩
+        have hf:= f.2.2 ⟨m, Nat.add_lt_add_iff_right.mp h⟩
         simp only [ne_eq, Fin.ext_iff] at hf
         omega
     · simp only [succ_eq_add_one, ne_eq, f']
@@ -505,13 +484,9 @@ def involutionNoFixedSetOne {n : ℕ} :
     ext i
     simp only
     split
-    · simp only [Fin.val_one, succ_eq_add_one, Fin.zero_eta]
-      rw [f.2.2.2]
-      simp
-    · simp only [Fin.val_zero, succ_eq_add_one, Fin.mk_one]
-      rw [hf1]
-      simp
-    · rfl
+    · simp [Fin.val_one, succ_eq_add_one, Fin.zero_eta, f.2.2.2]
+    · exact congrArg Fin.val (id (Eq.symm hf1))
+    · exact rfl
   right_inv f := by
     simp only [ne_eq, mul_eq, succ_eq_add_one, Function.comp_apply]
     ext i
@@ -521,8 +496,7 @@ def involutionNoFixedSetOne {n : ℕ} :
       simp [Fin.ext_iff] at h
     · rename_i h
       simp [Fin.ext_iff] at h
-    · rename_i h
-      simp only [Fin.val_succ, add_tsub_cancel_right]
+    · simp only [Fin.val_succ, add_tsub_cancel_right]
       congr
       apply congrArg
       simp_all [Fin.ext_iff]
@@ -552,8 +526,7 @@ def involutionNoFixedZeroEquivProd {n : ℕ} :
     ≃ Fin n.succ ×
     {f : Fin n → Fin n // Function.Involutive f ∧ (∀ i, f i ≠ i)} := by
   refine Equiv.trans involutionNoFixedEquivSumSame ?_
-  exact Equiv.sigmaEquivProd (Fin n.succ)
-      { f // Function.Involutive f ∧ ∀ (i : Fin n), f i ≠ i}
+  exact Equiv.sigmaEquivProd (Fin n.succ) { f // Function.Involutive f ∧ ∀ (i : Fin n), f i ≠ i }
 
 /-!
 

HepLean/Mathematics/List.lean

@@ -707,7 +707,7 @@ lemma eraseIdx_get {I : Type} (l : List I) (i : Fin l.length) :
   ext x
   simp only [Function.comp_apply, List.get_eq_getElem, List.eraseIdx, List.getElem_eraseIdx]
   simp only [Fin.succAbove, Fin.coe_cast]
-  by_cases hi: x.castSucc < Fin.cast (by exact Eq.symm (eraseIdx_length l i)) i
+  by_cases hi: x.castSucc < Fin.cast (Eq.symm (eraseIdx_length l i)) i
   · simp only [hi, ↓reduceIte, Fin.coe_castSucc, dite_eq_left_iff, not_lt]
     intro h
     rw [Fin.lt_def] at hi

HepLean/Mathematics/List/InsertionSort.lean

@@ -34,7 +34,7 @@ lemma insertionSortMin_lt_mem_insertionSortDropMinPos {α : Type} (r : α → α
     (i : Fin (insertionSortDropMinPos r a l).length) :
     r (insertionSortMin r a l) ((insertionSortDropMinPos r a l)[i]) := by
   let l1 := List.insertionSort r (a :: l)
-  have hl1 : l1.Sorted r := by exact List.sorted_insertionSort r (a :: l)
+  have hl1 : l1.Sorted r := List.sorted_insertionSort r (a :: l)
   simp only [l1] at hl1
   rw [insertionSort_eq_insertionSortMin_cons r a l] at hl1
   simp only [List.sorted_cons, List.mem_insertionSort] at hl1