refactor: Golfing

HepLean/AnomalyCancellation/SM/Basic.lean

@@ -43,19 +43,16 @@ def toSpeciesEquiv : (SMCharges n).charges ≃ (Fin 5 → Fin n → ℚ) :=
 @[simps!]
 def toSpecies (i : Fin 5) : (SMCharges n).charges →ₗ[ℚ] (SMSpecies n).charges where
   toFun S := toSpeciesEquiv S i
-  map_add' _ _ := by aesop
-  map_smul' _ _ := by aesop
+  map_add' _ _ := by rfl
+  map_smul' _ _ := by rfl
 
 lemma charges_eq_toSpecies_eq (S T : (SMCharges n).charges) :
     S = T ↔ ∀ i, toSpecies i S = toSpecies i T := by
   apply Iff.intro
-  intro h
-  rw [h]
-  simp only [forall_const]
+  exact fun a i => congrArg (⇑(toSpecies i)) a
   intro h
   apply toSpeciesEquiv.injective
-  funext i
-  exact h i
+  exact (Set.eqOn_univ (toSpeciesEquiv S) (toSpeciesEquiv T)).mp fun ⦃x⦄ a => h x
 
 lemma toSMSpecies_toSpecies_inv (i : Fin 5) (f :  (Fin 5 → Fin n → ℚ) ) :
     (toSpecies i) (toSpeciesEquiv.symm f) = f i := by
@@ -142,8 +139,7 @@ lemma accSU2_ext {S T : (SMCharges n).charges}
     AddHom.coe_mk]
   repeat erw [Finset.sum_add_distrib]
   repeat erw [← Finset.mul_sum]
-  repeat erw [hj]
-  rfl
+  exact Mathlib.Tactic.LinearCombination.add_pf (congrArg (HMul.hMul 3) (hj 0)) (hj 3)
 
 /-- The `SU(3)` anomaly equations. -/
 @[simp]

HepLean/AnomalyCancellation/SM/NoGrav/One/LinearParameterization.lean

@@ -107,7 +107,7 @@ lemma cubic_zero_E'_zero (S : linearParameters) (hc : accCube (S.asCharges) = 0)
   rw [h1] at hc
   simp at hc
   cases' hc with hc hc
-  have h2 := (add_eq_zero_iff' (by nlinarith) (by nlinarith)).mp hc
+  have h2 := (add_eq_zero_iff' (by nlinarith) (sq_nonneg S.Y)).mp hc
   simp at h2
   exact h2.1
   exact hc
@@ -120,8 +120,6 @@ def bijection : linearParameters ≃ (SMNoGrav 1).LinSols where
      SMCharges.E S.val (0 : Fin 1)⟩
   left_inv S := by
     apply linearParameters.ext
-    simp only [Fin.isValue, toSpecies_apply]
-    repeat erw [speciesVal]
     rfl
     repeat erw [speciesVal]
     simp only [Fin.isValue]
@@ -243,7 +241,7 @@ def bijectionLinearParameters :
     have hvw := S.hvw
     have hQ := S.hx
     apply linearParametersQENeqZero.ext
-    simp only [tolinearParametersQNeqZero_x, toLinearParameters_coe_Q']
+    rfl
     field_simp
     ring
     simp only [tolinearParametersQNeqZero_w, toLinearParameters_coe_Y, toLinearParameters_coe_Q',
@@ -255,7 +253,7 @@ def bijectionLinearParameters :
     have hQ := S.2.1
     have hE := S.2.2
     apply linearParameters.ext
-    simp only [ne_eq, toLinearParameters_coe_Q', tolinearParametersQNeqZero_x]
+    rfl
     field_simp
     ring_nf
     field_simp [hQ, hE]
@@ -283,7 +281,7 @@ lemma cubic (S : linearParametersQENeqZero) :
     ring
   rw [h1]
   simp_all
-  rw [add_eq_zero_iff_eq_neg]
+  exact add_eq_zero_iff_eq_neg
 
 
 lemma cubic_v_or_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
@@ -294,8 +292,8 @@ lemma cubic_v_or_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection
   rw [← h1] at h
   by_contra hn
   simp [not_or] at hn
-  have h2 := FLTThree S.v S.w (-1) hn.1 hn.2 (by simp)
-  simp_all
+  have h2 := FLTThree S.v S.w (-1) hn.1 hn.2 (Ne.symm (ne_of_beq_false (by rfl)))
+  exact h2 h
 
 lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
     (hv : S.v = 0 ) : S.w = -1 := by
@@ -303,8 +301,7 @@ lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.
   simp at h
   have h' : (S.w + 1) * (1 * S.w * S.w + (-1) * S.w + 1) = 0 := by
     ring_nf
-    rw [add_comm]
-    exact add_eq_zero_iff_eq_neg.mpr h
+    exact add_eq_zero_iff_neg_eq.mpr (id (Eq.symm h))
   have h'' : (1 * S.w * S.w + (-1) * S.w + 1)  ≠ 0 := by
     refine quadratic_ne_zero_of_discrim_ne_sq ?_ S.w
     intro s
@@ -314,7 +311,7 @@ lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.
       simp [discrim]
     nlinarith
   simp_all
-  linear_combination h'
+  exact eq_neg_of_add_eq_zero_left h'
 
 lemma cube_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
     (hw : S.w = 0 ) : S.v = -1 := by
@@ -322,8 +319,7 @@ lemma cube_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.v
   simp at h
   have h' : (S.v + 1) * (1 * S.v * S.v + (-1) * S.v + 1) = 0 := by
     ring_nf
-    rw [add_comm]
-    exact add_eq_zero_iff_eq_neg.mpr h
+    exact add_eq_zero_iff_neg_eq.mpr (id (Eq.symm h))
   have h'' : (1 * S.v * S.v + (-1) * S.v + 1)  ≠ 0 := by
     refine quadratic_ne_zero_of_discrim_ne_sq ?_ S.v
     intro s
@@ -333,7 +329,7 @@ lemma cube_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.v
       simp [discrim]
     nlinarith
   simp_all
-  linear_combination h'
+  exact eq_neg_of_add_eq_zero_left h'
 
 lemma cube_w_v (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
     (FLTThree : FermatLastTheoremWith ℚ 3) :
@@ -356,7 +352,7 @@ lemma grav (S : linearParametersQENeqZero) : accGrav (bijection S).1.val = 0 ↔
   linear_combination -1 * h / 6
   intro h
   rw [h]
-  ring
+  exact Eq.symm (mul_neg_one (6 * S.x))
 
 lemma grav_of_cubic (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
     (FLTThree : FermatLastTheoremWith ℚ 3) :
@@ -365,9 +361,9 @@ lemma grav_of_cubic (S : linearParametersQENeqZero) (h : accCube (bijection S).1
   have h' := cube_w_v S h FLTThree
   cases' h' with h h
   rw [h.1, h.2]
-  simp only [add_zero]
+  exact Rat.add_zero (-1)
   rw [h.1, h.2]
-  simp
+  exact Rat.zero_add (-1)
 
 end linearParametersQENeqZero
 

HepLean/AnomalyCancellation/SM/Permutations.lean

@@ -38,19 +38,8 @@ instance : Group (permGroup n) := Pi.group
 @[simps!]
 def chargeMap (f : permGroup n) : (SMCharges n).charges →ₗ[ℚ] (SMCharges n).charges where
   toFun S := toSpeciesEquiv.symm (fun i => toSpecies i S ∘ f i )
-  map_add' S T := by
-    simp only
-    rw [charges_eq_toSpecies_eq]
-    intro i
-    rw [(toSpecies i).map_add]
-    rw [toSMSpecies_toSpecies_inv, toSMSpecies_toSpecies_inv, toSMSpecies_toSpecies_inv]
-    rfl
-  map_smul' a S := by
-    simp only
-    rw [charges_eq_toSpecies_eq]
-    intro i
-    rw [(toSpecies i).map_smul, toSMSpecies_toSpecies_inv, toSMSpecies_toSpecies_inv]
-    rfl
+  map_add' _ _ := rfl
+  map_smul' _ _ := rfl
 
 /-- The representation of `(permGroup n)` acting on the vector space of charges. -/
 @[simp]
@@ -81,10 +70,10 @@ lemma repCharges_toSpecies (f : permGroup n) (S : (SMCharges n).charges) (j : Fi
 lemma toSpecies_sum_invariant (m : ℕ) (f : permGroup n) (S : (SMCharges n).charges) (j : Fin 5) :
     ∑ i, ((fun a => a ^ m) ∘ toSpecies j (repCharges f S)) i =
     ∑ i, ((fun a => a ^ m) ∘ toSpecies j S) i := by
-  erw [repCharges_toSpecies]
-  change  ∑ i : Fin n, ((fun a => a ^ m) ∘ _) (⇑(f⁻¹ _) i) = ∑ i : Fin n, ((fun a => a ^ m) ∘ _) i
-  refine Equiv.Perm.sum_comp _ _ _ ?_
-  simp only [permGroup, Fin.isValue, Pi.inv_apply, ne_eq, coe_univ, Set.subset_univ]
+  rw [repCharges_toSpecies]
+  exact Fintype.sum_equiv (f⁻¹ j) (fun x => ((fun a => a ^ m) ∘ (toSpecies j) S ∘ ⇑(f⁻¹ j)) x)
+   (fun x => ((fun a => a ^ m) ∘ (toSpecies j) S) x) (congrFun rfl)
+
 
 
 lemma accGrav_invariant (f : permGroup n) (S : (SMCharges n).charges)  :
@@ -116,7 +105,6 @@ lemma accQuad_invariant (f : permGroup n) (S : (SMCharges n).charges)  :
 
 lemma accCube_invariant (f : permGroup n) (S : (SMCharges n).charges)  :
     accCube (repCharges f S) = accCube S :=
-  accCube_ext
-    (by simpa using toSpecies_sum_invariant 3 f S)
+  accCube_ext (fun j => toSpecies_sum_invariant 3 f S j)
 
 end SM