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docs: More acc documentation

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jstoobysmith 2024-11-27 14:35:02 +00:00
parent d582979013
commit 371e402570
3 changed files with 11 additions and 1 deletions
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8
HepLean/AnomalyCancellation/SM/NoGrav/One/Lemmas.lean
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@ -25,6 +25,8 @@ open SMCharges
open SMACCs
open BigOperators
/-- For a set of 1 family SM charges satisfying all ACCs except the gravitational,
the charge of `Q` is zero if and only if `E` is zero. -/
lemma E_zero_iff_Q_zero {S : (SMNoGrav 1).Sols} : Q S.val (0 : Fin 1) = 0 ↔
E S.val (0 : Fin 1) = 0 := by
let S' := linearParameters.bijection.symm S.1.1
@ -34,6 +36,8 @@ lemma E_zero_iff_Q_zero {S : (SMNoGrav 1).Sols} : Q S.val (0 : Fin 1) = 0 ↔
rw [← hS'] at hC
exact Iff.intro (fun hQ => S'.cubic_zero_Q'_zero hC hQ) (fun hE => S'.cubic_zero_E'_zero hC hE)
/-- For a set of 1-family SM charges satisfying all ACCs except the gravitational,
if the `Q` charge is zero then the charges satisfy the gravitional ACCs. -/
lemma accGrav_Q_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) = 0) :
accGrav S.val = 0 := by
rw [accGrav]
@ -48,6 +52,8 @@ lemma accGrav_Q_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) = 0) :
simp_all
linear_combination 3 * h2
/-- For a set of 1-family SM charges satisfying all ACCs except the gravitational,
if the `Q` charge is not zero then the charges satisfy the gravitional ACCs. -/
lemma accGrav_Q_neq_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) ≠ 0) :
accGrav S.val = 0 := by
have hE := E_zero_iff_Q_zero.mpr.mt hQ
@ -59,7 +65,7 @@ lemma accGrav_Q_neq_zero {S : (SMNoGrav 1).Sols} (hQ : Q S.val (0 : Fin 1) ≠ 0
rw [← hS'] at hC ⊢
exact S'.grav_of_cubic hC
/-- Any solution to the ACCs without gravity satisfies the gravitational ACC. -/
/-- Any solution to the 1-family ACCs without gravity satisfies the gravitational ACC. -/
theorem accGravSatisfied {S : (SMNoGrav 1).Sols} :
accGrav S.val = 0 := by
by_cases hQ : Q S.val (0 : Fin 1)= 0