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refactor: replace some simp with exact

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jstoobysmith 2024-08-30 10:43:29 -04:00
parent 167145acef
commit 81f3566be8
13 changed files with 82 additions and 102 deletions
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18
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/ToSols.lean
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@ -73,7 +73,7 @@ lemma linEqPropSol_iff_proj_linEqProp (R : MSSMACC.Sols) :
rw [α₁_proj, α₂_proj, h]
simp only [neg_zero, Fin.isValue, Fin.reduceFinMk, zero_mul, and_self]
· rw [h.2.2]
simp
exact Rat.mul_zero ((dot Y₃.val) B₃.val)
/-- A condition which is satisfied if the plane spanned by `R`, `Y₃` and `B₃` lies
entirely in the quadratic surface. -/
@ -119,7 +119,7 @@ lemma inQuadSolProp_iff_proj_inQuadProp (R : MSSMACC.Sols) :
simp only [Fin.isValue, Fin.reduceFinMk, mul_eq_zero,
OfNat.ofNat_ne_zero, or_self, false_or] at h
rw [h.2.1, h.2.2]
simp
exact Prod.mk_eq_zero.mp rfl
/-- A condition which is satisfied if the plane spanned by `R`, `Y₃` and `B₃` lies
entirely in the cubic surface. -/
@ -166,7 +166,7 @@ lemma inCubeSolProp_iff_proj_inCubeProp (R : MSSMACC.Sols) :
simp only [Fin.isValue, Fin.reduceFinMk, mul_eq_zero, OfNat.ofNat_ne_zero, ne_eq,
not_false_eq_true, pow_eq_zero_iff, or_self, false_or] at h
rw [h.2.1, h.2.2]
simp
exact Prod.mk_eq_zero.mp rfl
/-- Those charge assignments perpendicular to `Y₃` and `B₃` which satisfy the condition
`lineEqProp`. -/
@ -215,7 +215,7 @@ lemma toSolNSQuad_eq_planeY₃B₃_on_α (R : MSSMACC.AnomalyFreePerp) :
apply planeY₃B₃_eq
rw [α₁, α₂, α₃]
ring_nf
simp
exact ⟨trivial, trivial, trivial⟩
/-- Given an `R` perpendicular to `Y₃` and `B₃`, an element of `Sols`. This map is
not surjective. -/
@ -243,7 +243,7 @@ lemma toSolNS_proj (T : NotInLineEqSol) : toSolNS (toSolNSProj T.val) = T.val :=
rw [h1]
have h1 := (lineEqPropSol_iff_lineEqCoeff_zero T.val).mpr.mt T.prop
rw [← MulAction.mul_smul, mul_comm, mul_inv_cancel h1]
simp
exact MulAction.one_smul T.1.val
/-- A solution to the ACCs, given an element of `inLineEq × ℚ × ℚ × ℚ`. -/
def inLineEqToSol : InLineEq × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R, c₁, c₂, c₃) =>
@ -286,7 +286,7 @@ lemma inLineEqToSol_proj (T : InLineEqSol) : inLineEqToSol (inLineEqProj T) = T.
rw [h1]
have h2 := (inQuadSolProp_iff_quadCoeff_zero T.val).mpr.mt T.prop.2
rw [← MulAction.mul_smul, mul_comm, mul_inv_cancel h2]
simp
exact MulAction.one_smul T.1.val
/-- Given an element of `inQuad × ℚ × ℚ × ℚ`, a solution to the ACCs. -/
def inQuadToSol : InQuad × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R, a₁, a₂, a₃) =>
@ -331,7 +331,7 @@ lemma inQuadToSol_proj (T : InQuadSol) : inQuadToSol (inQuadProj T) = T.val := b
rw [h1]
have h2 := (inCubeSolProp_iff_cubicCoeff_zero T.val).mpr.mt T.prop.2.2
rw [← MulAction.mul_smul, mul_comm, mul_inv_cancel h2]
simp
exact MulAction.one_smul T.1.val
/-- Given a element of `inQuadCube × ℚ × ℚ × ℚ`, a solution to the ACCs. -/
def inQuadCubeToSol : InQuadCube × ℚ × ℚ × ℚ → MSSMACC.Sols := fun (R, b₁, b₂, b₃) =>
@ -371,9 +371,9 @@ lemma inQuadCubeToSol_proj (T : InQuadCubeSol) :
ring_nf
simp only [Fin.isValue, Fin.reduceFinMk, zero_smul, add_zero, zero_add]
rw [← MulAction.mul_smul, mul_comm, mul_inv_cancel]
· simp only [one_smul]
· exact MulAction.one_smul (T.1).val
· rw [show dot Y₃.val B₃.val = 108 by rfl]
simp
exact Ne.symm (OfNat.zero_ne_ofNat 108)
/-- A solution from an element of `MSSMACC.AnomalyFreePerp × ℚ × ℚ × ℚ`. We will
show that this map is a surjection. -/