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refactor: more simp to simp only

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jstoobysmith 2024-09-09 06:01:25 -04:00
parent 2c00ebba9b
commit 2792027a7f
9 changed files with 59 additions and 50 deletions
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30
HepLean/AnomalyCancellation/SM/NoGrav/One/LinearParameterization.lean
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@ -95,20 +95,20 @@ lemma cubic (S : linearParameters) :
lemma cubic_zero_Q'_zero (S : linearParameters) (hc : accCube (S.asCharges) = 0)
(h : S.Q' = 0) : S.E' = 0 := by
rw [cubic, h] at hc
simp at hc
exact hc
simpa using hc
lemma cubic_zero_E'_zero (S : linearParameters) (hc : accCube (S.asCharges) = 0)
(h : S.E' = 0) : S.Q' = 0 := by
rw [cubic, h] at hc
simp at hc
simp only [neg_mul, ne_eq, OfNat.ofNat_ne_zero, not_false_eq_true, zero_pow, add_zero] at hc
have h1 : -(54 * S.Q' ^ 3) - 18 * S.Q' * S.Y ^ 2 = - 18 * (3 * S.Q' ^ 2 + S.Y ^ 2) * S.Q' := by
ring
rw [h1] at hc
simp at hc
simp only [neg_mul, neg_eq_zero, mul_eq_zero, OfNat.ofNat_ne_zero, false_or] at hc
cases' hc with hc hc
· have h2 := (add_eq_zero_iff_of_nonneg (by nlinarith) (sq_nonneg S.Y)).mp hc
simp at h2
simp only [mul_eq_zero, OfNat.ofNat_ne_zero, ne_eq, not_false_eq_true, pow_eq_zero_iff,
false_or] at h2
exact h2.1
· exact hc
@ -140,9 +140,13 @@ def bijection : linearParameters ≃ (SMNoGrav 1).LinSols where
subst hj
erw [speciesVal]
have h1 := SU3Sol S
simp at h1
simp only [accSU3, SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero,
Fin.isValue, toSpecies_apply, Nat.reduceMul, Finset.sum_singleton, Prod.mk_zero_zero,
LinearMap.coe_mk, AddHom.coe_mk] at h1
have h2 := SU2Sol S
simp at h2
simp only [accSU2, SMSpecies_numberCharges, Finset.univ_unique, Fin.default_eq_zero,
Fin.isValue, toSpecies_apply, Nat.reduceMul, Finset.sum_singleton, Prod.mk_zero_zero,
LinearMap.coe_mk, AddHom.coe_mk] at h2
match i with
| 0 => rfl
| 1 =>
@ -282,14 +286,14 @@ lemma cubic_v_or_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection
have h1 : (-1)^3 = (-1 : ℚ) := by rfl
rw [← h1] at h
by_contra hn
simp [not_or] at hn
rw [not_or] at hn
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
rw [S.cubic, hv] at h
simp at h
simp only [ne_eq, OfNat.ofNat_ne_zero, not_false_eq_true, zero_pow, zero_add] at h
have h' : (S.w + 1) * (1 * S.w * S.w + (-1) * S.w + 1) = 0 := by
ring_nf
exact add_eq_zero_iff_neg_eq.mpr (id (Eq.symm h))
@ -307,7 +311,7 @@ lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.
lemma cube_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
(hw : S.w = 0) : S.v = -1 := by
rw [S.cubic, hw] at h
simp at h
simp only [ne_eq, OfNat.ofNat_ne_zero, not_false_eq_true, zero_pow, add_zero] at h
have h' : (S.v + 1) * (1 * S.v * S.v + (-1) * S.v + 1) = 0 := by
ring_nf
exact add_eq_zero_iff_neg_eq.mpr (id (Eq.symm h))
@ -327,10 +331,8 @@ 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
· simpa [hx] using cubic_v_zero S h hx
· simpa [hx] using 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]