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refactor: Lint

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jstoobysmith 2024-07-19 17:00:32 -04:00
parent 52e591fa7a
commit 9f27a3a9fd
46 changed files with 176 additions and 168 deletions
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24
HepLean/AnomalyCancellation/PureU1/Even/BasisLinear.lean
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@ -550,7 +550,7 @@ def Pa' (f : (Fin n.succ) ⊕ (Fin n) → ℚ) : (PureU1 (2 * n.succ)).LinSols :
∑ i, f i • basisa i
lemma Pa'_P'_P!' (f : (Fin n.succ) ⊕ (Fin n) → ℚ) :
Pa' f = P' (f ∘ Sum.inl) + P!' (f ∘ Sum.inr):= by
Pa' f = P' (f ∘ Sum.inl) + P!' (f ∘ Sum.inr) := by
exact Fintype.sum_sum_type _
lemma P'_val (f : Fin n.succ → ℚ) : (P' f).val = P f := by
@ -617,7 +617,7 @@ lemma Pa'_eq (f f' : (Fin n.succ) ⊕ (Fin n) → ℚ) : Pa' f = Pa' f' ↔ f =
simp
have h2 : ∀ i, (f i + (- f' i)) = 0 := by
exact Fintype.linearIndependent_iff.mp (@basisa_linear_independent n)
(fun i => f i + -f' i) h1
(fun i => f i + -f' i) h1
have h2i := h2 i
linarith
intro h
@ -685,9 +685,9 @@ lemma span_basis (S : (PureU1 (2 * n.succ)).LinSols) :
rfl
lemma P!_in_span (f : Fin n → ℚ) : P! f ∈ Submodule.span ℚ (Set.range basis!AsCharges) := by
rw [(mem_span_range_iff_exists_fun ℚ)]
use f
rfl
rw [(mem_span_range_iff_exists_fun ℚ)]
use f
rfl
lemma smul_basis!AsCharges_in_span (S : (PureU1 (2 * n.succ)).LinSols) (j : Fin n) :
(S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j ∈
@ -700,11 +700,9 @@ lemma smul_basis!AsCharges_in_span (S : (PureU1 (2 * n.succ)).LinSols) (j : Fin
lemma span_basis_swap! {S : (PureU1 (2 * n.succ)).LinSols} (j : Fin n)
(hS : ((FamilyPermutations (2 * n.succ)).linSolRep
(pairSwap (δ!₁ j) (δ!₂ j))) S = S') (g : Fin n.succ → ℚ) (f : Fin n → ℚ)
(h : S.val = P g + P! f):
∃
(g' : Fin n.succ → ℚ) (f' : Fin n → ℚ),
S'.val = P g' + P! f' ∧ P! f' = P! f +
(S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j ∧ g' = g := by
(h : S.val = P g + P! f) : ∃ (g' : Fin n.succ → ℚ) (f' : Fin n → ℚ),
S'.val = P g' + P! f' ∧ P! f' = P! f +
(S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j ∧ g' = g := by
let X := P! f + (S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j
have hX : X ∈ Submodule.span ℚ (Set.range (basis!AsCharges)) := by
apply Submodule.add_mem
@ -723,10 +721,8 @@ lemma span_basis_swap! {S : (PureU1 (2 * n.succ)).LinSols} (j : Fin n)
exact hS
lemma vectorLikeEven_in_span (S : (PureU1 (2 * n.succ)).LinSols)
(hS : VectorLikeEven S.val) :
∃ (M : (FamilyPermutations (2 * n.succ)).group),
(FamilyPermutations (2 * n.succ)).linSolRep M S
∈ Submodule.span ℚ (Set.range basis) := by
(hS : VectorLikeEven S.val) : ∃ (M : (FamilyPermutations (2 * n.succ)).group),
(FamilyPermutations (2 * n.succ)).linSolRep M S ∈ Submodule.span ℚ (Set.range basis) := by
use (Tuple.sort S.val).symm
change sortAFL S ∈ Submodule.span ℚ (Set.range basis)
rw [mem_span_range_iff_exists_fun ℚ]