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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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32
HepLean/AnomalyCancellation/PureU1/Even/BasisLinear.lean
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@ -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 :