refactor: Lint
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3 changed files with 12 additions and 6 deletions
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@ -381,7 +381,8 @@ lemma equivCons_trans {n m k : ℕ} (e : Fin n ≃ Fin m) (f : Fin m ≃ Fin k)
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Fin.equivCons (e.trans f) = (Fin.equivCons e).trans (Fin.equivCons f) := by
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refine Equiv.ext_iff.mpr ?_
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intro x
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simp [Fin.equivCons]
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simp only [Nat.succ_eq_add_one, equivCons, Equiv.toFun_as_coe, Equiv.coe_trans,
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Equiv.invFun_as_coe, Equiv.coe_fn_mk, Equiv.trans_apply]
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match x with
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| ⟨0, h⟩ => rfl
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| ⟨i + 1, h⟩ => rfl
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@ -391,7 +392,9 @@ lemma equivCons_castOrderIso {n m : ℕ} (h : n = m) :
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(Fin.equivCons (Fin.castOrderIso h).toEquiv) = (Fin.castOrderIso (by simp [h])).toEquiv := by
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refine Equiv.ext_iff.mpr ?_
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intro x
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simp [Fin.equivCons]
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simp only [Nat.succ_eq_add_one, equivCons, Equiv.toFun_as_coe, RelIso.coe_fn_toEquiv,
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Equiv.invFun_as_coe, OrderIso.toEquiv_symm, Fin.symm_castOrderIso, Equiv.coe_fn_mk,
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Fin.castOrderIso_apply]
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match x with
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| ⟨0, h⟩ => rfl
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| ⟨i + 1, h⟩ => rfl
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@ -399,7 +402,8 @@ lemma equivCons_castOrderIso {n m : ℕ} (h : n = m) :
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@[simp]
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lemma equivCons_symm_succ {n m : ℕ} (e : Fin n ≃ Fin m) (i : ℕ) (hi : i + 1 < m.succ) :
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(Fin.equivCons e).symm ⟨i + 1, hi⟩ = (e.symm ⟨i, Nat.succ_lt_succ_iff.mp hi⟩).succ := by
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simp [Fin.equivCons]
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simp only [Nat.succ_eq_add_one, equivCons, Equiv.toFun_as_coe, Equiv.invFun_as_coe,
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Equiv.coe_fn_symm_mk]
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have hi : ⟨i + 1, hi⟩ = Fin.succ ⟨i, Nat.succ_lt_succ_iff.mp hi⟩ := by rfl
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rw [hi]
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rw [Fin.cons_succ]
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@ -80,12 +80,15 @@ lemma insertEquiv_get {α : Type} {r : α → α → Prop} [DecidableRel r] (a :
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trans (b :: List.orderedInsert r a l).get ∘ Fin.cast (by
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rw [List.orderedInsert_length]
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simp [List.orderedInsert_length])
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· simp
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· simp only [List.orderedInsert.eq_2, List.length_cons, Fin.zero_eta, Fin.mk_one]
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ext x
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match x with
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| ⟨0, h⟩ => rfl
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| ⟨Nat.succ x, h⟩ =>
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simp
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simp only [Nat.succ_eq_add_one, Function.comp_apply, Equiv.symm_trans_apply,
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Equiv.symm_swap, OrderIso.toEquiv_symm, Fin.symm_castOrderIso, RelIso.coe_fn_toEquiv,
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Fin.castOrderIso_apply, Fin.cast_mk, equivCons_symm_succ, List.get_eq_getElem,
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List.length_cons, List.getElem_cons_succ]
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have hswap (n : Fin (b :: a :: l).length) :
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(a :: b :: l).get (Equiv.swap ⟨0, by simp⟩ ⟨1, by simp⟩ n) = (b :: a :: l).get n := by
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match n with
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