{"name":"MSSMACC.α₃_proj","declaration":"theorem MSSMACC.α₃_proj (T : ACCSystem.Sols MSSMACC) : MSSMACC.α₃ (MSSMACC.proj T.toLinSols) =\n  6 * (MSSMACC.dot MSSMACC.Y₃.val) MSSMACC.B₃.val ^ 3 *\n    (((MSSMACCs.cubeTriLin T.val) T.val) MSSMACC.Y₃.val * (MSSMACCs.quadBiLin MSSMACC.B₃.val) T.val -\n      ((MSSMACCs.cubeTriLin T.val) T.val) MSSMACC.B₃.val * (MSSMACCs.quadBiLin MSSMACC.Y₃.val) T.val)"}
{"name":"MSSMACC.lineCube_smul","declaration":"theorem MSSMACC.lineCube_smul (R : MSSMACC.AnomalyFreePerp) (a : ℚ) (b : ℚ) (c : ℚ) (d : ℚ) : MSSMACC.lineCube R (d * a) (d * b) (d * c) = d • MSSMACC.lineCube R a b c"}
{"name":"MSSMACC.lineQuadAFL","declaration":"/-- The line in the plane spanned by `Y₃`, `B₃` and `R` which is in the quadratic,\nas `LinSols`. -/\ndef MSSMACC.lineQuadAFL (R : MSSMACC.AnomalyFreePerp) (c1 : ℚ) (c2 : ℚ) (c3 : ℚ) : ACCSystemLinear.LinSols MSSMACC.toACCSystemLinear"}
{"name":"MSSMACC.lineQuad","declaration":"/-- The line in the plane spanned by `Y₃`, `B₃` and `R` which is in the quadratic. -/\ndef MSSMACC.lineQuad (R : MSSMACC.AnomalyFreePerp) (c1 : ℚ) (c2 : ℚ) (c3 : ℚ) : ACCSystemQuad.QuadSols MSSMACC.toACCSystemQuad"}
{"name":"MSSMACC.planeY₃B₃_val","declaration":"theorem MSSMACC.planeY₃B₃_val (R : MSSMACC.AnomalyFreePerp) (a : ℚ) (b : ℚ) (c : ℚ) : (MSSMACC.planeY₃B₃ R a b c).val = a • MSSMACC.Y₃.val + b • MSSMACC.B₃.val + c • R.val"}
{"name":"MSSMACC.α₁_proj","declaration":"theorem MSSMACC.α₁_proj (T : ACCSystem.Sols MSSMACC) : MSSMACC.α₁ (MSSMACC.proj T.toLinSols) =\n  -MSSMACC.α₃ (MSSMACC.proj T.toLinSols) * ((MSSMACC.dot MSSMACC.B₃.val) T.val - (MSSMACC.dot MSSMACC.Y₃.val) T.val)"}
{"name":"MSSMACC.α₂_proj","declaration":"theorem MSSMACC.α₂_proj (T : ACCSystem.Sols MSSMACC) : MSSMACC.α₂ (MSSMACC.proj T.toLinSols) =\n  -MSSMACC.α₃ (MSSMACC.proj T.toLinSols) * ((MSSMACC.dot MSSMACC.Y₃.val) T.val - 2 * (MSSMACC.dot MSSMACC.B₃.val) T.val)"}
{"name":"MSSMACC.planeY₃B₃_cubic","declaration":"theorem MSSMACC.planeY₃B₃_cubic (R : MSSMACC.AnomalyFreePerp) (a : ℚ) (b : ℚ) (c : ℚ) : MSSMACCs.accCube (MSSMACC.planeY₃B₃ R a b c).val =\n  c ^ 2 *\n    (3 * a * ((MSSMACCs.cubeTriLin R.val) R.val) MSSMACC.Y₃.val +\n        3 * b * ((MSSMACCs.cubeTriLin R.val) R.val) MSSMACC.B₃.val +\n      c * ((MSSMACCs.cubeTriLin R.val) R.val) R.val)"}
{"name":"MSSMACC.planeY₃B₃_val_eq'","declaration":"theorem MSSMACC.planeY₃B₃_val_eq' {a' : ℚ} {b' : ℚ} {c' : ℚ} (R : MSSMACC.AnomalyFreePerp) (a : ℚ) (b : ℚ) (c : ℚ) (hR' : R.val ≠ 0) (h : (MSSMACC.planeY₃B₃ R a b c).val = (MSSMACC.planeY₃B₃ R a' b' c').val) : a = a' ∧ b = b' ∧ c = c'"}
{"name":"MSSMACC.lineCube","declaration":"/-- The line in the plane spanned by `Y₃`, `B₃` and `R` which is in the cubic. -/\ndef MSSMACC.lineCube (R : MSSMACC.AnomalyFreePerp) (a₁ : ℚ) (a₂ : ℚ) (a₃ : ℚ) : ACCSystemLinear.LinSols MSSMACC.toACCSystemLinear"}
{"name":"MSSMACC.α₂","declaration":"/-- A helper function to simplify following expressions. -/\ndef MSSMACC.α₂ (T : MSSMACC.AnomalyFreePerp) : ℚ"}
{"name":"MSSMACC.planeY₃B₃_smul","declaration":"theorem MSSMACC.planeY₃B₃_smul (R : MSSMACC.AnomalyFreePerp) (a : ℚ) (b : ℚ) (c : ℚ) (d : ℚ) : MSSMACC.planeY₃B₃ R (d * a) (d * b) (d * c) = d • MSSMACC.planeY₃B₃ R a b c"}
{"name":"MSSMACC.lineQuadAFL_quad","declaration":"theorem MSSMACC.lineQuadAFL_quad (R : MSSMACC.AnomalyFreePerp) (c1 : ℚ) (c2 : ℚ) (c3 : ℚ) : MSSMACCs.accQuad (MSSMACC.lineQuadAFL R c1 c2 c3).val = 0"}
{"name":"MSSMACC.planeY₃B₃_quad","declaration":"theorem MSSMACC.planeY₃B₃_quad (R : MSSMACC.AnomalyFreePerp) (a : ℚ) (b : ℚ) (c : ℚ) : MSSMACCs.accQuad (MSSMACC.planeY₃B₃ R a b c).val =\n  c *\n    (2 * a * (MSSMACCs.quadBiLin MSSMACC.Y₃.val) R.val + 2 * b * (MSSMACCs.quadBiLin MSSMACC.B₃.val) R.val +\n      c * (MSSMACCs.quadBiLin R.val) R.val)"}
{"name":"MSSMACC.α₁_proj_zero","declaration":"theorem MSSMACC.α₁_proj_zero (T : ACCSystem.Sols MSSMACC) (h1 : MSSMACC.α₃ (MSSMACC.proj T.toLinSols) = 0) : MSSMACC.α₁ (MSSMACC.proj T.toLinSols) = 0"}
{"name":"MSSMACC.lineQuad_cube","declaration":"theorem MSSMACC.lineQuad_cube (R : MSSMACC.AnomalyFreePerp) (c₁ : ℚ) (c₂ : ℚ) (c₃ : ℚ) : MSSMACCs.accCube (MSSMACC.lineQuad R c₁ c₂ c₃).val =\n  -4 * (c₁ * (MSSMACCs.quadBiLin MSSMACC.B₃.val) R.val - c₂ * (MSSMACCs.quadBiLin MSSMACC.Y₃.val) R.val) ^ 2 *\n    (MSSMACC.α₁ R * c₁ + MSSMACC.α₂ R * c₂ + MSSMACC.α₃ R * c₃)"}
{"name":"MSSMACC.lineQuad_smul","declaration":"theorem MSSMACC.lineQuad_smul (R : MSSMACC.AnomalyFreePerp) (a : ℚ) (b : ℚ) (c : ℚ) (d : ℚ) : MSSMACC.lineQuad R (d * a) (d * b) (d * c) = d • MSSMACC.lineQuad R a b c"}
{"name":"MSSMACC.lineCube_quad","declaration":"theorem MSSMACC.lineCube_quad (R : MSSMACC.AnomalyFreePerp) (a₁ : ℚ) (a₂ : ℚ) (a₃ : ℚ) : MSSMACCs.accQuad (MSSMACC.lineCube R a₁ a₂ a₃).val =\n  3 *\n      (a₁ * ((MSSMACCs.cubeTriLin R.val) R.val) MSSMACC.B₃.val -\n        a₂ * ((MSSMACCs.cubeTriLin R.val) R.val) MSSMACC.Y₃.val) *\n    (MSSMACC.α₁ R * a₁ + MSSMACC.α₂ R * a₂ + MSSMACC.α₃ R * a₃)"}
{"name":"MSSMACC.α₂_proj_zero","declaration":"theorem MSSMACC.α₂_proj_zero (T : ACCSystem.Sols MSSMACC) (h1 : MSSMACC.α₃ (MSSMACC.proj T.toLinSols) = 0) : MSSMACC.α₂ (MSSMACC.proj T.toLinSols) = 0"}
{"name":"MSSMACC.α₁","declaration":"/-- A helper function to simplify following expressions. -/\ndef MSSMACC.α₁ (T : MSSMACC.AnomalyFreePerp) : ℚ"}
{"name":"MSSMACC.planeY₃B₃","declaration":"/-- The plane of linear solutions spanned by `Y₃`, `B₃` and `R`, a point orthogonal\nto `Y₃` and `B₃`. -/\ndef MSSMACC.planeY₃B₃ (R : MSSMACC.AnomalyFreePerp) (a : ℚ) (b : ℚ) (c : ℚ) : ACCSystemLinear.LinSols MSSMACC.toACCSystemLinear"}
{"name":"MSSMACC.α₃","declaration":"/-- A helper function to simplify following expressions. -/\ndef MSSMACC.α₃ (T : MSSMACC.AnomalyFreePerp) : ℚ"}
{"name":"MSSMACC.lineQuad_val","declaration":"theorem MSSMACC.lineQuad_val (R : MSSMACC.AnomalyFreePerp) (c1 : ℚ) (c2 : ℚ) (c3 : ℚ) : (MSSMACC.lineQuad R c1 c2 c3).val =\n  (MSSMACC.planeY₃B₃ R (c2 * (MSSMACCs.quadBiLin R.val) R.val - 2 * c3 * (MSSMACCs.quadBiLin MSSMACC.B₃.val) R.val)\n      (2 * c3 * (MSSMACCs.quadBiLin MSSMACC.Y₃.val) R.val - c1 * (MSSMACCs.quadBiLin R.val) R.val)\n      (2 * c1 * (MSSMACCs.quadBiLin MSSMACC.B₃.val) R.val - 2 * c2 * (MSSMACCs.quadBiLin MSSMACC.Y₃.val) R.val)).val"}
{"name":"MSSMACC.planeY₃B₃_eq","declaration":"theorem MSSMACC.planeY₃B₃_eq {a' : ℚ} {b' : ℚ} {c' : ℚ} (R : MSSMACC.AnomalyFreePerp) (a : ℚ) (b : ℚ) (c : ℚ) (h : a = a' ∧ b = b' ∧ c = c') : MSSMACC.planeY₃B₃ R a b c = MSSMACC.planeY₃B₃ R a' b' c'"}
{"name":"MSSMACC.lineCube_cube","declaration":"theorem MSSMACC.lineCube_cube (R : MSSMACC.AnomalyFreePerp) (a₁ : ℚ) (a₂ : ℚ) (a₃ : ℚ) : MSSMACCs.accCube (MSSMACC.lineCube R a₁ a₂ a₃).val = 0"}