refactor: Simp lemmas

HepLean/AnomalyCancellation/PureU1/Basic.lean

@@ -31,7 +31,7 @@ def accGrav (n : ℕ) : ((PureU1Charges n).Charges →ₗ[ℚ] ℚ) where
   toFun S := ∑ i : Fin n, S i
   map_add' S T := Finset.sum_add_distrib
   map_smul' a S := by
-    simp [HSMul.hSMul, SMul.smul]
+    simp only [HSMul.hSMul, SMul.smul, eq_ratCast, Rat.cast_eq_id, id_eq]
     rw [← Finset.mul_sum]
 
 /-- The symmetric trilinear form used to define the cubic anomaly. -/
@@ -40,7 +40,7 @@ def accCubeTriLinSymm {n : ℕ} : TriLinearSymm (PureU1Charges n).Charges := Tri
   (fun S => ∑ i, S.1 i * S.2.1 i * S.2.2 i)
   (by
     intro a S L T
-    simp [HSMul.hSMul]
+    simp only [PureU1Charges_numberCharges, HSMul.hSMul, ACCSystemCharges.chargesModule_smul]
     rw [Finset.mul_sum]
     apply Fintype.sum_congr
     intro i
@@ -108,7 +108,7 @@ open BigOperators
 lemma pureU1_linear {n : ℕ} (S : (PureU1 n.succ).LinSols) :
     ∑ i, S.val i = 0 := by
   have hS := S.linearSol
-  simp at hS
+  simp only [succ_eq_add_one, PureU1_numberLinear, PureU1_linearACCs] at hS
   exact hS 0
 
 lemma pureU1_cube {n : ℕ} (S : (PureU1 n.succ).Sols) :
@@ -120,7 +120,7 @@ lemma pureU1_cube {n : ℕ} (S : (PureU1 n.succ).Sols) :
 lemma pureU1_last {n : ℕ} (S : (PureU1 n.succ).LinSols) :
     S.val (Fin.last n) = - ∑ i : Fin n, S.val i.castSucc := by
   have hS := pureU1_linear S
-  simp at hS
+  simp only [succ_eq_add_one, PureU1_numberCharges] at hS
   rw [Fin.sum_univ_castSucc] at hS
   linear_combination hS
 
@@ -134,7 +134,7 @@ lemma pureU1_anomalyFree_ext {n : ℕ} {S T : (PureU1 n.succ).LinSols}
     obtain ⟨j, hj⟩ := hiCast
     rw [← hj]
     exact h j
-  · simp at hi
+  · simp only [succ_eq_add_one, PureU1_numberCharges, ne_eq, Decidable.not_not] at hi
     rw [hi, pureU1_last, pureU1_last]
     simp only [neg_inj]
     apply Finset.sum_congr

HepLean/AnomalyCancellation/PureU1/Even/LineInCubic.lean

@@ -113,7 +113,7 @@ lemma P_P_P!_accCube' {S : (PureU1 (2 * n.succ.succ)).LinSols}
   have h1 := Pa_δ!₄ f g
   have h2 := Pa_δ!₁ f g (Fin.last n)
   have h3 := Pa_δ!₂ f g (Fin.last n)
-  simp at h1 h2 h3
+  simp only [Fin.succ_last, Nat.succ_eq_add_one] at h1 h2 h3
   have hl : f (Fin.succ (Fin.last n)) = - Pa f g δ!₄ := by
     simp_all only [Fin.succ_last, neg_neg]
   erw [hl] at h2
@@ -133,7 +133,7 @@ lemma lineInCubicPerm_last_cond {S : (PureU1 (2 * n.succ.succ)).LinSols}
   obtain ⟨g, f, hfg⟩ := span_basis S
   have h1 := lineInCubicPerm_swap LIC (Fin.last n) g f hfg
   rw [P_P_P!_accCube' g f hfg] at h1
-  simp 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
     linear_combination h1
@@ -148,7 +148,8 @@ lemma lineInCubicPerm_last_perm {S : (PureU1 (2 * n.succ.succ)).LinSols}
     δ!₄ ?_ ?_ ?_ ?_
   · simp [Fin.ext_iff, δ!₂, δ!₁]
   · simp [Fin.ext_iff, δ!₂, δ!₄]
-  · simp [Fin.ext_iff, δ!₁, δ!₄]
+  · simp only [Nat.succ_eq_add_one, δ!₁, δ!₄, Fin.isValue, ne_eq, Fin.ext_iff, Fin.coe_cast,
+    Fin.coe_natAdd, Fin.coe_castAdd, Fin.val_last, Fin.coe_fin_one, add_zero, add_right_inj]
     omega
   · exact fun M => lineInCubicPerm_last_cond (lineInCubicPerm_permute LIC M)
 

HepLean/AnomalyCancellation/PureU1/LineInPlaneCond.lean

@@ -58,14 +58,18 @@ lemma lineInPlaneCond_eq_last' {S : (PureU1 (n.succ.succ)).LinSols} (hS : LineIn
   erw [sq_eq_sq_iff_eq_or_eq_neg] at h
   rw [LineInPlaneCond] at hS
   simp only [LineInPlaneProp] at hS
-  simp [not_or] at h
+  simp only [Nat.succ_eq_add_one, Fin.succ_last, not_or] at h
   have h1 (i : Fin n) : S.val i.castSucc.castSucc =
       - (S.val ((Fin.last n).castSucc) + (S.val ((Fin.last n).succ))) / 2 := by
     have h1S := hS (Fin.last n).castSucc ((Fin.last n).succ) i.castSucc.castSucc
-      (by simp; rw [Fin.ext_iff]; exact Nat.ne_add_one ↑(Fin.last n).castSucc)
-      (by simp; rw [Fin.ext_iff]; simp; omega)
-      (by simp; rw [Fin.ext_iff]; simp; omega)
-    simp_all
+      (by simp only [Fin.ext_iff, Nat.succ_eq_add_one, Fin.succ_last, ne_eq]
+          exact Nat.ne_add_one ↑(Fin.last n).castSucc)
+      (by simp only [Nat.succ_eq_add_one, Fin.succ_last, ne_eq, Fin.ext_iff, Fin.val_last,
+        Fin.coe_castSucc]
+          omega)
+      (by simp only [Nat.succ_eq_add_one, ne_eq, Fin.ext_iff, Fin.coe_castSucc, Fin.val_last]
+          omega)
+    simp_all only [Nat.succ_eq_add_one, ne_eq, Fin.succ_last, false_or, neg_add_rev]
     field_simp
     linear_combination h1S
   have h2 := pureU1_last S
@@ -152,7 +156,7 @@ lemma linesInPlane_four (S : (PureU1 4).Sols) (hS : LineInPlaneCond S.1.1) :
       rw [h4, h5] at hcube
       have h6 : S.val (3 : Fin 4) ^ 3 = 0 := by
         linear_combination -1 * hcube / 24
-      simp at h6
+      simp only [Fin.isValue, ne_eq, OfNat.ofNat_ne_zero, not_false_eq_true, pow_eq_zero_iff] at h6
       simp_all
 
 lemma linesInPlane_eq_sq_four {S : (PureU1 4).Sols}

HepLean/AnomalyCancellation/PureU1/Odd/Parameterization.lean

@@ -60,7 +60,7 @@ lemma parameterizationCharge_cube (g f : Fin n → ℚ) (a : ℚ) :
 /-- Given a `g f : Fin n → ℚ` and a `a : ℚ` we form a solution. -/
 def parameterization (g f : Fin n → ℚ) (a : ℚ) :
     (PureU1 (2 * n + 1)).Sols :=
-  ⟨⟨parameterizationAsLinear g f a, by intro i; simp at i; exact Fin.elim0 i⟩,
+  ⟨⟨parameterizationAsLinear g f a, fun i => Fin.elim0 i⟩,
   parameterizationCharge_cube g f a⟩
 
 lemma anomalyFree_param {S : (PureU1 (2 * n + 1)).Sols}
@@ -125,13 +125,10 @@ theorem generic_case {S : (PureU1 (2 * n.succ + 1)).Sols} (h : GenericCase S) :
   apply ACCSystem.Sols.ext
   rw [parameterizationAsLinear_val]
   change S.val = _ • (_ • P g + _• P! f)
-  rw [anomalyFree_param _ _ hS]
-  rw [neg_neg, ← smul_add, smul_smul, inv_mul_cancel₀, one_smul]
+  rw [anomalyFree_param _ _ hS, neg_neg, ← smul_add, smul_smul, inv_mul_cancel₀, one_smul]
   · exact hS
-  · have h := h g f hS
-    rw [anomalyFree_param _ _ hS] at h
-    simp at h
-    exact h
+  · simpa only [Nat.succ_eq_add_one, accCubeTriLinSymm_toFun_apply_apply, ne_eq,
+      anomalyFree_param _ _ hS, neg_eq_zero] using h g f hS
 
 lemma special_case_lineInCubic {S : (PureU1 (2 * n.succ + 1)).Sols}
     (h : SpecialCase S) :
@@ -139,15 +136,13 @@ lemma special_case_lineInCubic {S : (PureU1 (2 * n.succ + 1)).Sols}
   intro g f hS a b
   erw [TriLinearSymm.toCubic_add]
   rw [HomogeneousCubic.map_smul, HomogeneousCubic.map_smul]
-  erw [P_accCube]
-  erw [P!_accCube]
+  erw [P_accCube, P!_accCube]
   have h := h g f hS
   rw [accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
     accCubeTriLinSymm.map_smul₃, accCubeTriLinSymm.map_smul₁, accCubeTriLinSymm.map_smul₂,
-    accCubeTriLinSymm.map_smul₃]
-  rw [h]
+    accCubeTriLinSymm.map_smul₃, h]
   rw [anomalyFree_param _ _ hS] at h
-  simp at h
+  simp only [Nat.succ_eq_add_one, accCubeTriLinSymm_toFun_apply_apply, neg_eq_zero] at h
   change accCubeTriLinSymm (P! f) (P! f) (P g) = 0 at h
   erw [h]
   simp

HepLean/AnomalyCancellation/SMNu/PlusU1/HyperCharge.lean

@@ -33,7 +33,7 @@ def Y₁ : (PlusU1 1).Sols where
     | (5 : Fin 6) => 0
   linearSol := by
     intro i
-    simp at i
+    simp only [PlusU1_numberLinear] at i
     match i with
     | 0 => rfl
     | 1 => rfl
@@ -41,7 +41,7 @@ def Y₁ : (PlusU1 1).Sols where
     | 3 => rfl
   quadSol := by
     intro i
-    simp at i
+    simp only [PlusU1_numberQuadratic] at i
     match i with
     | 0 => rfl
   cubicSol := by rfl