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refactor: Golfing

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jstoobysmith 2024-06-13 08:10:08 -04:00
parent fbda420da9
commit d7b6cf7246
13 changed files with 73 additions and 117 deletions
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30
HepLean/AnomalyCancellation/SM/NoGrav/One/LinearParameterization.lean
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@ -107,7 +107,7 @@ lemma cubic_zero_E'_zero (S : linearParameters) (hc : accCube (S.asCharges) = 0)
rw [h1] at hc
simp at hc
cases' hc with hc hc
have h2 := (add_eq_zero_iff' (by nlinarith) (by nlinarith)).mp hc
have h2 := (add_eq_zero_iff' (by nlinarith) (sq_nonneg S.Y)).mp hc
simp at h2
exact h2.1
exact hc
@ -120,8 +120,6 @@ def bijection : linearParameters ≃ (SMNoGrav 1).LinSols where
SMCharges.E S.val (0 : Fin 1)⟩
left_inv S := by
apply linearParameters.ext
simp only [Fin.isValue, toSpecies_apply]
repeat erw [speciesVal]
rfl
repeat erw [speciesVal]
simp only [Fin.isValue]
@ -243,7 +241,7 @@ def bijectionLinearParameters :
have hvw := S.hvw
have hQ := S.hx
apply linearParametersQENeqZero.ext
simp only [tolinearParametersQNeqZero_x, toLinearParameters_coe_Q']
rfl
field_simp
ring
simp only [tolinearParametersQNeqZero_w, toLinearParameters_coe_Y, toLinearParameters_coe_Q',
@ -255,7 +253,7 @@ def bijectionLinearParameters :
have hQ := S.2.1
have hE := S.2.2
apply linearParameters.ext
simp only [ne_eq, toLinearParameters_coe_Q', tolinearParametersQNeqZero_x]
rfl
field_simp
ring_nf
field_simp [hQ, hE]
@ -283,7 +281,7 @@ lemma cubic (S : linearParametersQENeqZero) :
ring
rw [h1]
simp_all
rw [add_eq_zero_iff_eq_neg]
exact add_eq_zero_iff_eq_neg
lemma cubic_v_or_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
@ -294,8 +292,8 @@ lemma cubic_v_or_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection
rw [← h1] at h
by_contra hn
simp [not_or] at hn
have h2 := FLTThree S.v S.w (-1) hn.1 hn.2 (by simp)
simp_all
have h2 := FLTThree S.v S.w (-1) hn.1 hn.2 (Ne.symm (ne_of_beq_false (by rfl)))
exact h2 h
lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
(hv : S.v = 0 ) : S.w = -1 := by
@ -303,8 +301,7 @@ lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.
simp at h
have h' : (S.w + 1) * (1 * S.w * S.w + (-1) * S.w + 1) = 0 := by
ring_nf
rw [add_comm]
exact add_eq_zero_iff_eq_neg.mpr h
exact add_eq_zero_iff_neg_eq.mpr (id (Eq.symm h))
have h'' : (1 * S.w * S.w + (-1) * S.w + 1) ≠ 0 := by
refine quadratic_ne_zero_of_discrim_ne_sq ?_ S.w
intro s
@ -314,7 +311,7 @@ lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.
simp [discrim]
nlinarith
simp_all
linear_combination h'
exact eq_neg_of_add_eq_zero_left h'
lemma cube_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
(hw : S.w = 0 ) : S.v = -1 := by
@ -322,8 +319,7 @@ lemma cube_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.v
simp at h
have h' : (S.v + 1) * (1 * S.v * S.v + (-1) * S.v + 1) = 0 := by
ring_nf
rw [add_comm]
exact add_eq_zero_iff_eq_neg.mpr h
exact add_eq_zero_iff_neg_eq.mpr (id (Eq.symm h))
have h'' : (1 * S.v * S.v + (-1) * S.v + 1) ≠ 0 := by
refine quadratic_ne_zero_of_discrim_ne_sq ?_ S.v
intro s
@ -333,7 +329,7 @@ lemma cube_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.v
simp [discrim]
nlinarith
simp_all
linear_combination h'
exact eq_neg_of_add_eq_zero_left h'
lemma cube_w_v (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
(FLTThree : FermatLastTheoremWith ℚ 3) :
@ -356,7 +352,7 @@ lemma grav (S : linearParametersQENeqZero) : accGrav (bijection S).1.val = 0 ↔
linear_combination -1 * h / 6
intro h
rw [h]
ring
exact Eq.symm (mul_neg_one (6 * S.x))
lemma grav_of_cubic (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
(FLTThree : FermatLastTheoremWith ℚ 3) :
@ -365,9 +361,9 @@ lemma grav_of_cubic (S : linearParametersQENeqZero) (h : accCube (bijection S).1
have h' := cube_w_v S h FLTThree
cases' h' with h h
rw [h.1, h.2]
simp only [add_zero]
exact Rat.add_zero (-1)
rw [h.1, h.2]
simp
exact Rat.zero_add (-1)
end linearParametersQENeqZero