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refactor: replace simps

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jstoobysmith 2024-08-30 11:52:27 -04:00
parent 81f3566be8
commit cd04e13ced
6 changed files with 43 additions and 45 deletions
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8
HepLean/AnomalyCancellation/PureU1/ConstAbs.lean
View file

@ -121,7 +121,7 @@ lemma boundary_accGrav'' (k : Fin n) (hk : Boundary S k) :
rw [Fin.sum_univ_add]
have hfst (i : Fin k.succ.val) :
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)
apply lt_eq hS (le_of_lt hk.left) (Fin.is_le i)
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
apply gt_eq hS (le_of_lt hk.right) (by rw [Fin.le_def]; exact le.intro rfl)
@ -144,7 +144,7 @@ lemma not_hasBoundary_zero_le (hnot : ¬ (HasBoundary S)) (h0 : S (0 : Fin n.suc
· rfl
· rename_i i hii
have hnott := hnot ⟨i, succ_lt_succ_iff.mp hi⟩
have hii := hii (by omega)
have hii := hii (lt_of_succ_lt hi)
erw [← hii] at hnott
exact (val_le_zero hS (hnott h0)).symm
@ -212,7 +212,7 @@ lemma AFL_even_below' {A : (PureU1 (2 * n.succ)).LinSols} (h : ConstAbsSorted A.
rw [Fin.le_def]
simp only [PureU1_numberCharges, Fin.coe_cast, Fin.coe_castAdd, mul_eq, Fin.coe_castSucc]
rw [AFL_even_Boundary h hA hk]
omega
exact Fin.is_le i
lemma AFL_even_below (A : (PureU1 (2 * n.succ)).LinSols) (h : ConstAbsSorted A.val)
(i : Fin n.succ) :
@ -233,7 +233,7 @@ lemma AFL_even_above' {A : (PureU1 (2 * n.succ)).LinSols} (h : ConstAbsSorted A.
rw [Fin.le_def]
simp only [mul_eq, Fin.val_succ, PureU1_numberCharges, Fin.coe_cast, Fin.coe_natAdd]
rw [AFL_even_Boundary h hA hk]
omega
exact Nat.le_add_right (n + 1) ↑i
lemma AFL_even_above (A : (PureU1 (2 * n.succ)).LinSols) (h : ConstAbsSorted A.val)
(i : Fin n.succ) :

32
HepLean/AnomalyCancellation/PureU1/Even/BasisLinear.lean
View file

@ -71,9 +71,9 @@ lemma sum_δ₁_δ₂ (S : Fin (2 * n.succ) → ℚ) :
∑ i, S i = ∑ i : Fin n.succ, ((S ∘ δ₁) i + (S ∘ δ₂) i) := by
have h1 : ∑ i, S i = ∑ i : Fin (n.succ + n.succ), S (Fin.cast (split_equal n.succ) i) := by
rw [Finset.sum_equiv (Fin.castOrderIso (split_equal n.succ)).symm.toEquiv]
intro i
simp only [mem_univ, Fin.symm_castOrderIso, RelIso.coe_fn_toEquiv]
exact fun _ _=> rfl
· intro i
simp only [mem_univ, Fin.symm_castOrderIso, RelIso.coe_fn_toEquiv]
· exact fun _ _=> rfl
rw [h1]
rw [Fin.sum_univ_add, Finset.sum_add_distrib]
rfl
@ -82,9 +82,9 @@ lemma sum_δ₁_δ₂' (S : Fin (2 * n.succ) → ℚ) :
∑ i, S i = ∑ i : Fin n.succ, ((S ∘ δ₁) i + (S ∘ δ₂) i) := by
have h1 : ∑ i, S i = ∑ i : Fin (n.succ + n.succ), S (Fin.cast (split_equal n.succ) i) := by
rw [Finset.sum_equiv (Fin.castOrderIso (split_equal n.succ)).symm.toEquiv]
intro i
simp only [mem_univ, Fin.symm_castOrderIso, RelIso.coe_fn_toEquiv]
exact fun _ _ => rfl
· intro i
simp only [mem_univ, Fin.symm_castOrderIso, RelIso.coe_fn_toEquiv]
· exact fun _ _ => rfl
rw [h1]
rw [Fin.sum_univ_add, Finset.sum_add_distrib]
rfl
@ -93,9 +93,9 @@ lemma sum_δ!₁_δ!₂ (S : Fin (2 * n.succ) → ℚ) :
∑ i, S i = S δ!₃ + S δ!₄ + ∑ i : Fin n, ((S ∘ δ!₁) i + (S ∘ δ!₂) i) := by
have h1 : ∑ i, S i = ∑ i : Fin (1 + ((n + n) + 1)), S (Fin.cast (n_cond₂ n) i) := by
rw [Finset.sum_equiv (Fin.castOrderIso (n_cond₂ n)).symm.toEquiv]
intro i
simp only [mem_univ, Fin.symm_castOrderIso, RelIso.coe_fn_toEquiv]
exact fun _ _ => rfl
· intro i
simp only [mem_univ, Fin.symm_castOrderIso, RelIso.coe_fn_toEquiv]
· exact fun _ _ => rfl
rw [h1]
rw [Fin.sum_univ_add, Fin.sum_univ_add, Fin.sum_univ_add, Finset.sum_add_distrib]
simp only [univ_unique, Fin.default_eq_zero, Fin.isValue, sum_singleton, Function.comp_apply]
@ -108,12 +108,12 @@ lemma sum_δ!₁_δ!₂ (S : Fin (2 * n.succ) → ℚ) :
nth_rewrite 2 [Rat.add_comm]
rfl
lemma δ!₃_δ₁0 : @δ!₃ n = δ₁ 0 := by
rfl
lemma δ!₃_δ₁0 : @δ!₃ n = δ₁ 0 := rfl
lemma δ!₄_δ₂Last: @δ!₄ n = δ₂ (Fin.last n) := by
rw [Fin.ext_iff]
simp [δ!₄, δ₂]
simp only [succ_eq_add_one, δ!₄, Fin.isValue, Fin.coe_cast, Fin.coe_natAdd, Fin.coe_fin_one,
add_zero, δ₂, Fin.natAdd_last, Fin.val_last]
omega
lemma δ!₁_δ₁ (j : Fin n) : δ!₁ j = δ₁ j.succ := by
@ -511,10 +511,10 @@ lemma Pa_zero (f : Fin n.succ → ℚ) (g : Fin n → ℚ) (h : Pa f g = 0) :
induction iv
exact h₃.symm
rename_i iv hi
have hivi : iv < n.succ := by omega
have hivi : iv < n.succ := lt_of_succ_lt hiv
have hi2 := hi hivi
have h1 := Pa_δ!₁ f g ⟨iv, by omega⟩
have h2 := Pa_δ!₂ f g ⟨iv, by omega⟩
have h1 := Pa_δ!₁ f g ⟨iv, succ_lt_succ_iff.mp hiv⟩
have h2 := Pa_δ!₂ f g ⟨iv, succ_lt_succ_iff.mp hiv⟩
rw [h] at h1 h2
simp at h1 h2
erw [hi2] at h2
@ -648,7 +648,7 @@ lemma basisa_card : Fintype.card ((Fin n.succ) ⊕ (Fin n)) =
FiniteDimensional.finrank ℚ (PureU1 (2 * n.succ)).LinSols := by
erw [BasisLinear.finrank_AnomalyFreeLinear]
simp only [Fintype.card_sum, Fintype.card_fin, mul_eq]
omega
exact split_odd n
/-- The basis formed out of our `basisa` vectors. -/
noncomputable def basisaAsBasis :

2
HepLean/AnomalyCancellation/PureU1/LineInPlaneCond.lean
View file

@ -62,7 +62,7 @@ lemma lineInPlaneCond_eq_last' {S : (PureU1 (n.succ.succ)).LinSols} (hS : LineIn
have h1 (i : Fin n) : S.val i.castSucc.castSucc =
- (S.val ((Fin.last n).castSucc) + (S.val ((Fin.last n).succ))) / 2 := by
have h1S := hS (Fin.last n).castSucc ((Fin.last n).succ) i.castSucc.castSucc
(by simp; rw [Fin.ext_iff]; simp)
(by simp; rw [Fin.ext_iff]; exact Nat.ne_add_one ↑(Fin.last n).castSucc)
(by simp; rw [Fin.ext_iff]; simp; omega)
(by simp; rw [Fin.ext_iff]; simp; omega)
simp_all

32
HepLean/AnomalyCancellation/PureU1/Odd/BasisLinear.lean
View file

@ -82,7 +82,7 @@ lemma δa₁_δ!₃ : @δa₁ n = δ!₃ := by
lemma δa₂_δ₁ (j : Fin n) : δa₂ j = δ₁ j.succ := by
rw [Fin.ext_iff]
simp [δa₂, δ₁]
omega
exact Nat.add_comm 1 ↑j
lemma δa₂_δ!₁ (j : Fin n) : δa₂ j = δ!₁ j.castSucc := by
rw [Fin.ext_iff]
@ -91,7 +91,7 @@ lemma δa₂_δ!₁ (j : Fin n) : δa₂ j = δ!₁ j.castSucc := by
lemma δa₃_δ₃ : @δa₃ n = δ₃ := by
rw [Fin.ext_iff]
simp [δa₃, δ₃]
omega
exact Nat.add_comm 1 n
lemma δa₃_δ!₁ : δa₃ = δ!₁ (Fin.last n) := by
rfl
@ -99,7 +99,7 @@ lemma δa₃_δ!₁ : δa₃ = δ!₁ (Fin.last n) := by
lemma δa₄_δ₂ (j : Fin n.succ) : δa₄ j = δ₂ j := by
rw [Fin.ext_iff]
simp [δa₄, δ₂]
omega
exact Nat.add_comm 1 n
lemma δa₄_δ!₂ (j : Fin n.succ) : δa₄ j = δ!₂ j := by
rw [Fin.ext_iff]
@ -108,15 +108,15 @@ lemma δa₄_δ!₂ (j : Fin n.succ) : δa₄ j = δ!₂ j := by
lemma δ₂_δ!₂ (j : Fin n) : δ₂ j = δ!₂ j := by
rw [Fin.ext_iff]
simp [δ₂, δ!₂]
omega
exact Nat.add_comm n 1
lemma sum_δ (S : Fin (2 * n + 1) → ℚ) :
∑ i, S i = S δ₃ + ∑ i : Fin n, ((S ∘ δ₁) i + (S ∘ δ₂) i) := by
have h1 : ∑ i, S i = ∑ i : Fin (n + 1 + n), S (Fin.cast (split_odd n) i) := by
rw [Finset.sum_equiv (Fin.castOrderIso (split_odd n)).symm.toEquiv]
intro i
simp only [mem_univ, Fin.symm_castOrderIso, RelIso.coe_fn_toEquiv]
exact fun _ _ => rfl
· intro i
simp only [mem_univ, Fin.symm_castOrderIso, RelIso.coe_fn_toEquiv]
· exact fun _ _ => rfl
rw [h1]
rw [Fin.sum_univ_add, Fin.sum_univ_add]
simp only [univ_unique, Fin.default_eq_zero, Fin.isValue, sum_singleton, Function.comp_apply]
@ -129,14 +129,12 @@ lemma sum_δ! (S : Fin (2 * n + 1) → ℚ) :
∑ i, S i = S δ!₃ + ∑ i : Fin n, ((S ∘ δ!₁) i + (S ∘ δ!₂) i) := by
have h1 : ∑ i, S i = ∑ i : Fin ((1+n)+n), S (Fin.cast (split_odd! n) i) := by
rw [Finset.sum_equiv (Fin.castOrderIso (split_odd! n)).symm.toEquiv]
intro i
simp only [mem_univ, Fin.castOrderIso, RelIso.coe_fn_toEquiv]
exact fun _ _ => rfl
rw [h1]
rw [Fin.sum_univ_add, Fin.sum_univ_add]
· intro i
simp only [mem_univ, Fin.castOrderIso, RelIso.coe_fn_toEquiv]
· exact fun _ _ => rfl
rw [h1, Fin.sum_univ_add, Fin.sum_univ_add]
simp only [univ_unique, Fin.default_eq_zero, Fin.isValue, sum_singleton, Function.comp_apply]
rw [add_assoc]
rw [Finset.sum_add_distrib]
rw [add_assoc, Finset.sum_add_distrib]
rfl
end theDeltas
@ -503,13 +501,13 @@ lemma Pa_zero (f g : Fin n.succ → ℚ) (h : Pa f g = 0) :
induction iv
exact h₃.symm
rename_i iv hi
have hivi : iv < n.succ := by omega
have hivi : iv < n.succ := lt_of_succ_lt hiv
have hi2 := hi hivi
have h1 := Pa_δa₄ f g ⟨iv, hivi⟩
rw [h, hi2] at h1
change 0 = _ at h1
simp at h1
have h2 := Pa_δa₂ f g ⟨iv, by omega⟩
have h2 := Pa_δa₂ f g ⟨iv, succ_lt_succ_iff.mp hiv⟩
simp [h, h1] at h2
exact h2.symm
exact hinduc i.val i.prop
@ -643,7 +641,7 @@ lemma basisa_card : Fintype.card ((Fin n.succ) ⊕ (Fin n.succ)) =
FiniteDimensional.finrank ℚ (PureU1 (2 * n.succ + 1)).LinSols := by
erw [BasisLinear.finrank_AnomalyFreeLinear]
simp only [Fintype.card_sum, Fintype.card_fin]
omega
exact Eq.symm (Nat.two_mul n.succ)
/-- The basis formed out of our basisa vectors. -/
noncomputable def basisaAsBasis :

2
HepLean/AnomalyCancellation/SMNu/PlusU1/PlaneNonSols.lean
View file

@ -85,7 +85,7 @@ lemma Bi_sum_quad (i : Fin 11) (f : Fin 11 → ℚ) :
· rw [quadBiLin.map_smul₂]
· intro k hij
rw [quadBiLin.map_smul₂, Bi_Bj_quad hij.symm]
simp
exact Rat.mul_zero (f k)
/-- The coefficents of the quadratic equation in our basis. -/
@[simp]