mk_toList

proof body

Tactic-mode proof.

  67
  68end LeptonMassRatios
  69
  70namespace CkmMixingAngles
  71
  72/-- Canonical list view: `[V_us, V_cb, V_ub]`. -/
  73def toList (m : CkmMixingAngles) : List ℝ :=
  74  [m.vus, m.vcb, m.vub]
  75
  76@[simp] theorem toList_length (m : CkmMixingAngles) : m.toList.length = 3 := rfl
  77
  78/-- Every field satisfies a predicate. -/
  79def Forall (P : ℝ → Prop) (m : CkmMixingAngles) : Prop :=
  80  P m.vus ∧ P m.vcb ∧ P m.vub
  81
  82theorem forall_iff_list (P : ℝ → Prop) (m : CkmMixingAngles) :
  83    m.Forall P ↔ ∀ r ∈ m.toList, P r := by
  84  simp only [Forall, toList, List.mem_cons, List.mem_nil_iff, or_false]
  85  constructor
  86  · rintro ⟨h1, h2, h3⟩ r (rfl | rfl | rfl) <;> assumption
  87  · intro h
  88    exact ⟨h _ (Or.inl rfl), h _ (Or.inr (Or.inl rfl)), h _ (Or.inr (Or.inr rfl))⟩
  89
  90@[ext] theorem ext {a b : CkmMixingAngles}
  91    (h1 : a.vus = b.vus)
  92    (h2 : a.vcb = b.vcb)
  93    (h3 : a.vub = b.vub) : a = b := by
  94  cases a; cases b; simp_all
  95
  96theorem toList_injective {a b : CkmMixingAngles} (h : a.toList = b.toList) : a = b := by
  97  simp only [toList] at h
  98  have h1 : a.vus = b.vus := List.cons.inj h |>.1
  99  have h23 := List.cons.inj h |>.2
 100  have h2 : a.vcb = b.vcb := List.cons.inj h23 |>.1
 101  have h3 : a.vub = b.vub := List.cons.inj (List.cons.inj h23 |>.2) |>.1
 102  exact ext h1 h2 h3
 103
 104@[simp] theorem mk_toList (a b c : ℝ) :
 105    (⟨a, b, c⟩ : CkmMixingAngles).toList = [a, b, c] := rfl
 106
 107end CkmMixingAngles
 108
 109end RecogSpec
 110end IndisputableMonolith