refactor: Quad Lin equations

HepLean/AnomalyCancellation/SM/Basic.lean

@@ -208,21 +208,23 @@ lemma accYY_ext {S T : (SMCharges n).charges}
 
 /-- The quadratic bilinear map. -/
 @[simps!]
-def quadBiLin : BiLinearSymm (SMCharges n).charges where
-  toFun S := ∑ i, (Q S.1 i * Q S.2 i +
+def quadBiLin : BiLinearSymm (SMCharges n).charges := BiLinearSymm.mk₂
+  (fun S => ∑ i, (Q S.1 i * Q S.2 i +
     - 2 * (U S.1 i * U S.2 i) +
     D S.1 i * D S.2 i +
     (- 1) * (L S.1 i * L S.2 i) +
-    E S.1 i * E S.2 i)
-  map_smul₁' a S T := by
+    E S.1 i * E S.2 i))
+  (by
+    intro a S T
     simp only
     rw [Finset.mul_sum]
     apply Fintype.sum_congr
     intro i
     repeat erw [map_smul]
     simp [HSMul.hSMul, SMul.smul]
-    ring
-  map_add₁' S T R := by
+    ring)
+  (by
+    intro S1 S2 T
     simp only
     rw [← Finset.sum_add_distrib]
     apply Fintype.sum_congr
@@ -230,12 +232,13 @@ def quadBiLin : BiLinearSymm (SMCharges n).charges where
     repeat erw [map_add]
     simp only [ACCSystemCharges.chargesAddCommMonoid_add, toSpecies_apply, Fin.isValue, neg_mul,
       one_mul]
-    ring
-  swap' S T := by
+    ring)
+  (by
+    intro S T
     simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue, neg_mul, one_mul]
     apply Fintype.sum_congr
     intro i
-    ring
+    ring)
 
 /-- The quadratic anomaly cancellation condition. -/
 @[simp]
@@ -247,10 +250,10 @@ lemma accQuad_ext {S T : (SMCharges n).charges}
     (h : ∀ j, ∑ i, ((fun a => a^2) ∘ toSpecies j S) i =
     ∑ i, ((fun a => a^2) ∘ toSpecies j T) i) :
     accQuad S = accQuad T := by
-  simp only [accQuad, BiLinearSymm.toHomogeneousQuad_toFun, Fin.isValue]
+  simp only [HomogeneousQuadratic, accQuad, BiLinearSymm.toHomogeneousQuad_apply]
   erw [← quadBiLin.toFun_eq_coe]
   rw [quadBiLin]
-  simp only
+  simp only [quadBiLin, BiLinearSymm.mk₂, AddHom.toFun_eq_coe, AddHom.coe_mk, LinearMap.coe_mk]
   repeat erw [Finset.sum_add_distrib]
   repeat erw [← Finset.mul_sum]
   ring_nf
@@ -301,7 +304,7 @@ lemma accCube_ext {S T : (SMCharges n).charges}
     (h : ∀ j, ∑ i, ((fun a => a^3) ∘ toSpecies j S) i =
     ∑ i, ((fun a => a^3) ∘ toSpecies j T) i) :
     accCube S = accCube T := by
-  simp only [accCube, TriLinearSymm.toCubic_toFun, Fin.isValue]
+  simp only [HomogeneousCubic, accCube, TriLinearSymm.toCubic_apply]
   erw [← cubeTriLin.toFun_eq_coe]
   rw [cubeTriLin]
   simp only

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

@@ -84,9 +84,7 @@ lemma asLinear_val (S : linearParameters) : S.asLinear.val = S.asCharges := by
 
 lemma cubic (S : linearParameters) :
     accCube (S.asCharges) = - 54 * S.Q'^3 - 18 * S.Q' * S.Y ^ 2 + S.E'^3 := by
-  simp only [accCube, TriLinearSymm.toCubic_toFun, Finset.univ_unique,
-    Fin.default_eq_zero, Fin.isValue, asCharges, SMNoGrav_numberCharges, neg_add_rev, neg_mul,
-    Finset.sum_singleton]
+  simp only [HomogeneousCubic, accCube, TriLinearSymm.toCubic_apply, neg_mul]
   erw [← TriLinearSymm.toFun_eq_coe]
   rw [cubeTriLin]
   simp only [SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue,