chainFlux_zero_of_balanced

formal source

  69  ∀ u, phi L u = 0 := by
  70  intro u; simp [phi, hbal u, sub_self]
  71
  72lemma chainFlux_zero_of_balanced {M} (L : Ledger M) (ch : Chain M)
  73  (hbal : ∀ u, L.debit u = L.credit u) :
  74  chainFlux L ch = 0 := by
  75  simp [chainFlux, phi_zero_of_balanced (M:=M) L hbal]
  76
  77class AtomicTick (M : RecognitionStructure) where
  78  postedAt : Nat → M.U → Prop
  79  unique_post : ∀ t : Nat, ∃! u : M.U, postedAt t u
  80
  81theorem T2_atomicity {M} [AtomicTick M] :
  82  ∀ t u v, AtomicTick.postedAt (M:=M) t u → AtomicTick.postedAt (M:=M) t v → u = v := by
  83  intro t u v hu hv
  84  rcases (AtomicTick.unique_post (M:=M) t) with ⟨w, hw, huniq⟩
  85  have huw : u = w := huniq u hu
  86  have hvw : v = w := huniq v hv
  87  exact huw.trans hvw.symm
  88
  89end Recognition
  90
  91namespace Demo
  92
  93open Recognition
  94
  95structure U where
  96  a : Unit
  97
  98/-- Recognition relation by structural equality -/
  99def recog : U → U → Prop := fun x y => x = y
 100
 101def M : RecognitionStructure := { U := U, R := recog }
 102