{"name":"MSSMACC.AnomalyFreePerp.perpB₃","declaration":"def MSSMACC.AnomalyFreePerp.perpB₃ (self : MSSMACC.AnomalyFreePerp) : (MSSMACC.dot MSSMACC.B₃.val) self.val = 0"}
{"name":"MSSMACC.proj_val","declaration":"theorem MSSMACC.proj_val (T : ACCSystemLinear.LinSols MSSMACC.toACCSystemLinear) : (MSSMACC.proj T).val =\n  ((MSSMACC.dot MSSMACC.B₃.val) T.val - (MSSMACC.dot MSSMACC.Y₃.val) T.val) • MSSMACC.Y₃.val +\n      ((MSSMACC.dot MSSMACC.Y₃.val) T.val - 2 * (MSSMACC.dot MSSMACC.B₃.val) T.val) • MSSMACC.B₃.val +\n    (MSSMACC.dot MSSMACC.Y₃.val) MSSMACC.B₃.val • T.val"}
{"name":"MSSMACC.AnomalyFreePerp.mk","declaration":"ctor MSSMACC.AnomalyFreePerp.mk (toLinSols : ACCSystemLinear.LinSols MSSMACC.toACCSystemLinear) (perpY₃ : (MSSMACC.dot MSSMACC.Y₃.val) toLinSols.val = 0) (perpB₃ : (MSSMACC.dot MSSMACC.B₃.val) toLinSols.val = 0) : MSSMACC.AnomalyFreePerp"}
{"name":"MSSMACC.AnomalyFreePerp.perpY₃","declaration":"def MSSMACC.AnomalyFreePerp.perpY₃ (self : MSSMACC.AnomalyFreePerp) : (MSSMACC.dot MSSMACC.Y₃.val) self.val = 0"}
{"name":"MSSMACC.cube_proj_proj_B₃","declaration":"theorem MSSMACC.cube_proj_proj_B₃ (T : ACCSystemLinear.LinSols MSSMACC.toACCSystemLinear) : ((MSSMACCs.cubeTriLin (MSSMACC.proj T).val) (MSSMACC.proj T).val) MSSMACC.B₃.val =\n  (MSSMACC.dot MSSMACC.Y₃.val) MSSMACC.B₃.val ^ 2 * ((MSSMACCs.cubeTriLin T.val) T.val) MSSMACC.B₃.val"}
{"name":"MSSMACC.cube_proj_proj_Y₃","declaration":"theorem MSSMACC.cube_proj_proj_Y₃ (T : ACCSystemLinear.LinSols MSSMACC.toACCSystemLinear) : ((MSSMACCs.cubeTriLin (MSSMACC.proj T).val) (MSSMACC.proj T).val) MSSMACC.Y₃.val =\n  (MSSMACC.dot MSSMACC.Y₃.val) MSSMACC.B₃.val ^ 2 * ((MSSMACCs.cubeTriLin T.val) T.val) MSSMACC.Y₃.val"}
{"name":"MSSMACC.quad_self_proj","declaration":"theorem MSSMACC.quad_self_proj (T : ACCSystem.Sols MSSMACC) : (MSSMACCs.quadBiLin T.val) (MSSMACC.proj T.toLinSols).val =\n  ((MSSMACC.dot MSSMACC.B₃.val) T.val - (MSSMACC.dot MSSMACC.Y₃.val) T.val) *\n      (MSSMACCs.quadBiLin MSSMACC.Y₃.val) T.val +\n    ((MSSMACC.dot MSSMACC.Y₃.val) T.val - 2 * (MSSMACC.dot MSSMACC.B₃.val) T.val) *\n      (MSSMACCs.quadBiLin MSSMACC.B₃.val) T.val"}
{"name":"MSSMACC.proj","declaration":"/-- The projection of an object in `MSSMACC.AnomalyFreeLinear` onto the subspace\northgonal to `Y₃` and`B₃`. -/\ndef MSSMACC.proj (T : ACCSystemLinear.LinSols MSSMACC.toACCSystemLinear) : MSSMACC.AnomalyFreePerp"}
{"name":"MSSMACC.Y₃_plus_B₃_plus_proj","declaration":"theorem MSSMACC.Y₃_plus_B₃_plus_proj (T : ACCSystemLinear.LinSols MSSMACC.toACCSystemLinear) (a : ℚ) (b : ℚ) (c : ℚ) : a • MSSMACC.Y₃.val + b • MSSMACC.B₃.val + c • (MSSMACC.proj T).val =\n  (a + c * ((MSSMACC.dot MSSMACC.B₃.val) T.val - (MSSMACC.dot MSSMACC.Y₃.val) T.val)) • MSSMACC.Y₃.val +\n      (b + c * ((MSSMACC.dot MSSMACC.Y₃.val) T.val - 2 * (MSSMACC.dot MSSMACC.B₃.val) T.val)) • MSSMACC.B₃.val +\n    ((MSSMACC.dot MSSMACC.Y₃.val) MSSMACC.B₃.val * c) • T.val"}
{"name":"MSSMACC.AnomalyFreePerp","declaration":"/-- The type of linear solutions orthogonal to $Y_3$ and $B_3$. -/\nstructure MSSMACC.AnomalyFreePerp  : Type"}
{"name":"MSSMACC.quad_B₃_proj","declaration":"theorem MSSMACC.quad_B₃_proj (T : ACCSystemLinear.LinSols MSSMACC.toACCSystemLinear) : (MSSMACCs.quadBiLin MSSMACC.B₃.val) (MSSMACC.proj T).val =\n  (MSSMACC.dot MSSMACC.Y₃.val) MSSMACC.B₃.val * (MSSMACCs.quadBiLin MSSMACC.B₃.val) T.val"}
{"name":"MSSMACC.cube_proj_proj_self","declaration":"theorem MSSMACC.cube_proj_proj_self (T : ACCSystem.Sols MSSMACC) : ((MSSMACCs.cubeTriLin (MSSMACC.proj T.toLinSols).val) (MSSMACC.proj T.toLinSols).val) T.val =\n  2 * (MSSMACC.dot MSSMACC.Y₃.val) MSSMACC.B₃.val *\n    (((MSSMACC.dot MSSMACC.B₃.val) T.val - (MSSMACC.dot MSSMACC.Y₃.val) T.val) *\n        ((MSSMACCs.cubeTriLin T.val) T.val) MSSMACC.Y₃.val +\n      ((MSSMACC.dot MSSMACC.Y₃.val) T.val - 2 * (MSSMACC.dot MSSMACC.B₃.val) T.val) *\n        ((MSSMACCs.cubeTriLin T.val) T.val) MSSMACC.B₃.val)"}
{"name":"MSSMACC.cube_proj","declaration":"theorem MSSMACC.cube_proj (T : ACCSystem.Sols MSSMACC) : ((MSSMACCs.cubeTriLin (MSSMACC.proj T.toLinSols).val) (MSSMACC.proj T.toLinSols).val) (MSSMACC.proj T.toLinSols).val =\n  3 * (MSSMACC.dot MSSMACC.Y₃.val) MSSMACC.B₃.val ^ 2 *\n    (((MSSMACC.dot MSSMACC.B₃.val) T.val - (MSSMACC.dot MSSMACC.Y₃.val) T.val) *\n        ((MSSMACCs.cubeTriLin T.val) T.val) MSSMACC.Y₃.val +\n      ((MSSMACC.dot MSSMACC.Y₃.val) T.val - 2 * (MSSMACC.dot MSSMACC.B₃.val) T.val) *\n        ((MSSMACCs.cubeTriLin T.val) T.val) MSSMACC.B₃.val)"}
{"name":"MSSMACC.quad_Y₃_proj","declaration":"theorem MSSMACC.quad_Y₃_proj (T : ACCSystemLinear.LinSols MSSMACC.toACCSystemLinear) : (MSSMACCs.quadBiLin MSSMACC.Y₃.val) (MSSMACC.proj T).val =\n  (MSSMACC.dot MSSMACC.Y₃.val) MSSMACC.B₃.val * (MSSMACCs.quadBiLin MSSMACC.Y₃.val) T.val"}
{"name":"MSSMACC.quad_proj","declaration":"theorem MSSMACC.quad_proj (T : ACCSystem.Sols MSSMACC) : (MSSMACCs.quadBiLin (MSSMACC.proj T.toLinSols).val) (MSSMACC.proj T.toLinSols).val =\n  2 * (MSSMACC.dot MSSMACC.Y₃.val) MSSMACC.B₃.val *\n    (((MSSMACC.dot MSSMACC.B₃.val) T.val - (MSSMACC.dot MSSMACC.Y₃.val) T.val) *\n        (MSSMACCs.quadBiLin MSSMACC.Y₃.val) T.val +\n      ((MSSMACC.dot MSSMACC.Y₃.val) T.val - 2 * (MSSMACC.dot MSSMACC.B₃.val) T.val) *\n        (MSSMACCs.quadBiLin MSSMACC.B₃.val) T.val)"}