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refactor: def of symmetric trilin function

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jstoobysmith 2024-04-22 09:48:44 -04:00
parent 748bcb61ae
commit e36c61b331
24 changed files with 279 additions and 246 deletions
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20
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/Basic.lean
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@ -121,8 +121,8 @@ lemma quad_proj (T : MSSMACC.Sols) :
lemma cube_proj_proj_Y₃ (T : MSSMACC.LinSols) :
cubeTriLin ((proj T).val, (proj T).val, Y₃.val) =
(dot Y₃.val B₃.val)^2 * cubeTriLin (T.val, T.val, Y₃.val) := by
cubeTriLin (proj T).val (proj T).val Y₃.val =
(dot Y₃.val B₃.val)^2 * cubeTriLin T.val T.val Y₃.val := by
rw [proj_val]
rw [cubeTriLin.map_add₁, cubeTriLin.map_add₂]
erw [lineY₃B₃_doublePoint]
@ -143,8 +143,8 @@ lemma cube_proj_proj_Y₃ (T : MSSMACC.LinSols) :
ring
lemma cube_proj_proj_B₃ (T : MSSMACC.LinSols) :
cubeTriLin ((proj T).val, (proj T).val, B₃.val) =
(dot Y₃.val B₃.val)^2 * cubeTriLin (T.val, T.val, B₃.val) := by
cubeTriLin (proj T).val (proj T).val B₃.val =
(dot Y₃.val B₃.val)^2 * cubeTriLin T.val T.val B₃.val := by
rw [proj_val]
rw [cubeTriLin.map_add₁, cubeTriLin.map_add₂]
erw [lineY₃B₃_doublePoint]
@ -159,10 +159,10 @@ lemma cube_proj_proj_B₃ (T : MSSMACC.LinSols) :
ring
lemma cube_proj_proj_self (T : MSSMACC.Sols) :
cubeTriLin ((proj T.1.1).val, (proj T.1.1).val, T.val) =
cubeTriLin (proj T.1.1).val (proj T.1.1).val T.val =
2 * dot Y₃.val B₃.val *
((dot B₃.val T.val - dot Y₃.val T.val) * cubeTriLin (T.val, T.val, Y₃.val) +
( dot Y₃.val T.val- 2 * dot B₃.val T.val) * cubeTriLin (T.val, T.val, B₃.val)) := by
((dot B₃.val T.val - dot Y₃.val T.val) * cubeTriLin T.val T.val Y₃.val +
( dot Y₃.val T.val- 2 * dot B₃.val T.val) * cubeTriLin T.val T.val B₃.val) := by
rw [proj_val]
rw [cubeTriLin.map_add₁, cubeTriLin.map_add₂]
erw [lineY₃B₃_doublePoint]
@ -176,10 +176,10 @@ lemma cube_proj_proj_self (T : MSSMACC.Sols) :
ring
lemma cube_proj (T : MSSMACC.Sols) :
cubeTriLin ((proj T.1.1).val, (proj T.1.1).val, (proj T.1.1).val) =
cubeTriLin (proj T.1.1).val (proj T.1.1).val (proj T.1.1).val =
3 * dot Y₃.val B₃.val ^ 2 *
((dot B₃.val T.val - dot Y₃.val T.val) * cubeTriLin (T.val, T.val, Y₃.val) +
(dot Y₃.val T.val - 2 * dot B₃.val T.val) * cubeTriLin (T.val, T.val, B₃.val)) := by
((dot B₃.val T.val - dot Y₃.val T.val) * cubeTriLin T.val T.val Y₃.val +
(dot Y₃.val T.val - 2 * dot B₃.val T.val) * cubeTriLin T.val T.val B₃.val) := by
nth_rewrite 3 [proj_val]
repeat rw [cubeTriLin.map_add₃]
repeat rw [cubeTriLin.map_smul₃]