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feat: replace FLT sorry with assumptions

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jstoobysmith 2024-05-08 15:42:54 -04:00
parent 388c824463
commit 70cafbf41e
2 changed files with 14 additions and 10 deletions
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10
HepLean/AnomalyCancellation/SM/NoGrav/One/Lemmas.lean
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@ -54,7 +54,8 @@ lemma accGrav_Q_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) = 0) :
simp_all
linear_combination 3 * h2
lemma accGrav_Q_neq_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) ≠ 0) :
lemma accGrav_Q_neq_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) ≠ 0)
(FLTThree : FermatLastTheoremWith ℚ 3) :
accGrav S.val = 0 := by
have hE := E_zero_iff_Q_zero.mpr.mt hQ
let S' := linearParametersQENeqZero.bijection.symm ⟨S.1.1, And.intro hQ hE⟩
@ -64,13 +65,14 @@ lemma accGrav_Q_neq_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) ≠ 0
change _ = S.val at hS'
rw [← hS'] at hC
rw [← hS']
exact S'.grav_of_cubic hC
exact S'.grav_of_cubic hC FLTThree
/-- Any solution to the ACCs without gravity satifies the gravitational ACC. -/
theorem accGravSatisfied {S : (SMNoGrav 1).Sols} : accGrav S.val = 0 := by
theorem accGravSatisfied {S : (SMNoGrav 1).Sols} (FLTThree : FermatLastTheoremWith ℚ 3) :
accGrav S.val = 0 := by
by_cases hQ : Q S.val (0 : Fin 1)= 0
exact accGrav_Q_zero hQ
exact accGrav_Q_neq_zero hQ
exact accGrav_Q_neq_zero hQ FLTThree
end One