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reactor: Removal of double spaces

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jstoobysmith 2024-07-12 11:23:02 -04:00
parent ce92e1d649
commit 13f62a50eb
64 changed files with 550 additions and 546 deletions
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26
HepLean/AnomalyCancellation/PureU1/ConstAbs.lean
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@ -14,7 +14,7 @@ We look at charge assignments in which all charges have the same absolute value.
universe v u
open Nat
open Finset
open Finset
open BigOperators
namespace PureU1
@ -53,7 +53,7 @@ section charges
variable {S : (PureU1 n.succ).Charges} {A : (PureU1 n.succ).LinSols}
variable (hS : ConstAbsSorted S) (hA : ConstAbsSorted A.val)
lemma lt_eq {k i : Fin n.succ} (hk : S k ≤ 0) (hik : i ≤ k) : S i = S k := by
lemma lt_eq {k i : Fin n.succ} (hk : S k ≤ 0) (hik : i ≤ k) : S i = S k := by
have hSS := hS.2 i k hik
have ht := hS.1 i k
rw [sq_eq_sq_iff_eq_or_eq_neg] at ht
@ -61,7 +61,7 @@ lemma lt_eq {k i : Fin n.succ} (hk : S k ≤ 0) (hik : i ≤ k) : S i = S k :=
exact h
linarith
lemma val_le_zero {i : Fin n.succ} (hi : S i ≤ 0) : S i = S (0 : Fin n.succ) := by
lemma val_le_zero {i : Fin n.succ} (hi : S i ≤ 0) : S i = S (0 : Fin n.succ) := by
symm
apply lt_eq hS hi
simp
@ -108,7 +108,7 @@ lemma boundary_succ {k : Fin n} (hk : Boundary S k) : S k.succ = - S (0 : Fin n.
rw [opposite_signs_eq_neg hS (le_of_lt hk.left) (le_of_lt hk.right)] at hn
linear_combination -(1 * hn)
lemma boundary_split (k : Fin n) : k.succ.val + (n.succ - k.succ.val) = n.succ := by
lemma boundary_split (k : Fin n) : k.succ.val + (n.succ - k.succ.val) = n.succ := by
omega
lemma boundary_accGrav' (k : Fin n) : accGrav n.succ S =
@ -128,7 +128,7 @@ lemma boundary_accGrav'' (k : Fin n) (hk : Boundary S k) :
S (Fin.cast (boundary_split k) (Fin.castAdd (n.succ - k.succ.val) i)) = S k.castSucc := by
apply lt_eq hS (le_of_lt hk.left) (by rw [Fin.le_def]; simp; omega)
have hsnd (i : Fin (n.succ - k.succ.val)) :
S (Fin.cast (boundary_split k) (Fin.natAdd (k.succ.val) i)) = S k.succ := by
S (Fin.cast (boundary_split k) (Fin.natAdd (k.succ.val) i)) = S k.succ := by
apply gt_eq hS (le_of_lt hk.right) (by rw [Fin.le_def]; simp)
simp only [hfst, hsnd]
simp only [Fin.val_succ, sum_const, card_fin, nsmul_eq_mul, cast_add, cast_one,
@ -160,7 +160,7 @@ lemma not_hasBoundry_zero (hnot : ¬ (HasBoundary S)) (i : Fin n.succ) :
simp at hi
exact zero_gt hS hi i
lemma not_hasBoundary_grav (hnot : ¬ (HasBoundary S)) :
lemma not_hasBoundary_grav (hnot : ¬ (HasBoundary S)) :
accGrav n.succ S = n.succ * S (0 : Fin n.succ) := by
simp [accGrav, ← not_hasBoundry_zero hS hnot]
@ -196,7 +196,7 @@ lemma AFL_odd_zero {A : (PureU1 (2 * n + 1)).LinSols} (h : ConstAbsSorted A.val)
theorem AFL_odd (A : (PureU1 (2 * n + 1)).LinSols) (h : ConstAbsSorted A.val) :
A = 0 := by
apply ACCSystemLinear.LinSols.ext
exact is_zero h (AFL_odd_zero h)
exact is_zero h (AFL_odd_zero h)
lemma AFL_even_Boundary {A : (PureU1 (2 * n.succ)).LinSols} (h : ConstAbsSorted A.val)
(hA : A.val (0 : Fin (2 * n.succ)) ≠ 0) {k : Fin (2 * n + 1)} (hk : Boundary A.val k) :
@ -209,8 +209,8 @@ lemma AFL_even_Boundary {A : (PureU1 (2 * n.succ)).LinSols} (h : ConstAbsSorted
linear_combination h0 / 2
lemma AFL_even_below' {A : (PureU1 (2 * n.succ)).LinSols} (h : ConstAbsSorted A.val)
(hA : A.val (0 : Fin (2 * n.succ)) ≠ 0) (i : Fin n.succ) :
A.val (Fin.cast (split_equal n.succ) (Fin.castAdd n.succ i)) = A.val (0 : Fin (2*n.succ)) := by
(hA : A.val (0 : Fin (2 * n.succ)) ≠ 0) (i : Fin n.succ) :
A.val (Fin.cast (split_equal n.succ) (Fin.castAdd n.succ i)) = A.val (0 : Fin (2*n.succ)) := by
obtain ⟨k, hk⟩ := AFL_hasBoundary h hA
rw [← boundary_castSucc h hk]
apply lt_eq h (le_of_lt hk.left)
@ -221,7 +221,7 @@ lemma AFL_even_below' {A : (PureU1 (2 * n.succ)).LinSols} (h : ConstAbsSorted A.
lemma AFL_even_below (A : (PureU1 (2 * n.succ)).LinSols) (h : ConstAbsSorted A.val)
(i : Fin n.succ) :
A.val (Fin.cast (split_equal n.succ) (Fin.castAdd n.succ i))
A.val (Fin.cast (split_equal n.succ) (Fin.castAdd n.succ i))
= A.val (0 : Fin (2*n.succ)) := by
by_cases hA : A.val (0 : Fin (2*n.succ)) = 0
rw [is_zero h hA]
@ -230,8 +230,8 @@ lemma AFL_even_below (A : (PureU1 (2 * n.succ)).LinSols) (h : ConstAbsSorted A.v
exact AFL_even_below' h hA i
lemma AFL_even_above' {A : (PureU1 (2 * n.succ)).LinSols} (h : ConstAbsSorted A.val)
(hA : A.val (0 : Fin (2*n.succ)) ≠ 0) (i : Fin n.succ) :
A.val (Fin.cast (split_equal n.succ) (Fin.natAdd n.succ i)) =
(hA : A.val (0 : Fin (2*n.succ)) ≠ 0) (i : Fin n.succ) :
A.val (Fin.cast (split_equal n.succ) (Fin.natAdd n.succ i)) =
- A.val (0 : Fin (2*n.succ)) := by
obtain ⟨k, hk⟩ := AFL_hasBoundary h hA
rw [← boundary_succ h hk]
@ -243,7 +243,7 @@ lemma AFL_even_above' {A : (PureU1 (2 * n.succ)).LinSols} (h : ConstAbsSorted A.
lemma AFL_even_above (A : (PureU1 (2 * n.succ)).LinSols) (h : ConstAbsSorted A.val)
(i : Fin n.succ) :
A.val (Fin.cast (split_equal n.succ) (Fin.natAdd n.succ i)) =
A.val (Fin.cast (split_equal n.succ) (Fin.natAdd n.succ i)) =
- A.val (0 : Fin (2*n.succ)) := by
by_cases hA : A.val (0 : Fin (2*n.succ)) = 0
rw [is_zero h hA]