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refactor: more multiple-goals

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jstoobysmith 2024-08-20 15:27:45 -04:00
parent 01f9f7da8b
commit b9479c904d
4 changed files with 166 additions and 180 deletions
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78
HepLean/AnomalyCancellation/SM/NoGrav/One/LinearParameterization.lean
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@ -107,10 +107,10 @@ 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) (sq_nonneg S.Y)).mp hc
simp at h2
exact h2.1
exact hc
· have h2 := (add_eq_zero_iff' (by nlinarith) (sq_nonneg S.Y)).mp hc
simp at h2
exact h2.1
· exact hc
/-- The bijection between the type of linear parameters and `(SMNoGrav 1).LinSols`. -/
def bijection : linearParameters ≃ (SMNoGrav 1).LinSols where
@ -120,13 +120,13 @@ def bijection : linearParameters ≃ (SMNoGrav 1).LinSols where
SMCharges.E S.val (0 : Fin 1)⟩
left_inv S := by
apply linearParameters.ext
rfl
simp only [Fin.isValue]
repeat erw [speciesVal]
simp only [asCharges, neg_add_rev]
ring
simp only [toSpecies_apply]
rfl
· rfl
· simp only [Fin.isValue]
repeat erw [speciesVal]
simp only [asCharges, neg_add_rev]
ring
· simp only [toSpecies_apply]
rfl
right_inv S := by
simp only [Fin.isValue, toSpecies_apply]
apply ACCSystemLinear.LinSols.ext
@ -239,25 +239,25 @@ def bijectionLinearParameters :
have hvw := S.hvw
have hQ := S.hx
apply linearParametersQENeqZero.ext
rfl
field_simp
ring
simp only [tolinearParametersQNeqZero_w, toLinearParameters_coe_Y, toLinearParameters_coe_Q',
toLinearParameters_coe_E']
field_simp
ring
· rfl
· field_simp
ring
· simp only [tolinearParametersQNeqZero_w, toLinearParameters_coe_Y, toLinearParameters_coe_Q',
toLinearParameters_coe_E']
field_simp
ring
right_inv S := by
apply Subtype.ext
have hQ := S.2.1
have hE := S.2.2
apply linearParameters.ext
rfl
field_simp
ring_nf
field_simp [hQ, hE]
field_simp
ring_nf
field_simp [hQ, hE]
· rfl
· field_simp
ring_nf
field_simp [hQ, hE]
· field_simp
ring_nf
field_simp [hQ, hE]
/-- The bijection between `linearParametersQENeqZero` and `LinSols` with `Q` and `E` non-zero. -/
def bijection : linearParametersQENeqZero ≃
@ -332,23 +332,21 @@ lemma cube_w_v (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val
(S.v = -1 ∧ S.w = 0) ∨ (S.v = 0 ∧ S.w = -1) := by
have h' := cubic_v_or_w_zero S h FLTThree
cases' h' with hx hx
simp [hx]
exact cubic_v_zero S h hx
simp [hx]
exact cube_w_zero S h hx
· simp [hx]
exact cubic_v_zero S h hx
· simp [hx]
exact cube_w_zero S h hx
lemma grav (S : linearParametersQENeqZero) : accGrav (bijection S).1.val = 0 ↔ S.v + S.w = -1 := by
erw [linearParameters.grav]
have hvw := S.hvw
have hQ := S.hx
field_simp
apply Iff.intro
intro h
apply (mul_right_inj' hQ).mp
linear_combination -1 * h / 6
intro h
rw [h]
exact Eq.symm (mul_neg_one (6 * S.x))
refine Iff.intro (fun h => ?_) (fun h => ?_)
· apply (mul_right_inj' hQ).mp
linear_combination -1 * h / 6
· rw [h]
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) :
@ -356,10 +354,10 @@ lemma grav_of_cubic (S : linearParametersQENeqZero) (h : accCube (bijection S).1
rw [grav]
have h' := cube_w_v S h FLTThree
cases' h' with h h
rw [h.1, h.2]
exact Rat.add_zero (-1)
rw [h.1, h.2]
exact Rat.zero_add (-1)
· rw [h.1, h.2]
exact Rat.add_zero (-1)
· rw [h.1, h.2]
exact Rat.zero_add (-1)
end linearParametersQENeqZero