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chainFlux
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IndisputableMonolith.Chain on GitHub at line 40.
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37
38def phi {M} (L : Ledger M) : M.U → ℤ := fun u => L.debit u - L.credit u
39
40def chainFlux {M} (L : Ledger M) (ch : Chain M) : ℤ :=
41 phi L (ch.last) - phi L (ch.head)
42
43class Conserves {M} (L : Ledger M) : Prop where
44 conserve : ∀ ch : Chain M, ch.head = ch.last → chainFlux L ch = 0
45
46/-- ## T2 (Atomicity): unique posting per tick implies no collision at a tick. -/
47theorem T2_atomicity {M} [AtomicTick M] :
48 ∀ t u v, AtomicTick.postedAt (M:=M) t u → AtomicTick.postedAt (M:=M) t v → u = v := by
49 intro t u v hu hv
50 rcases (AtomicTick.unique_post (M:=M) t) with ⟨w, hw, huniq⟩
51 have hu' : u = w := huniq u hu
52 have hv' : v = w := huniq v hv
53 exact hu'.trans hv'.symm
54
55theorem T3_continuity {M} (L : Ledger M) [Conserves L] :
56 ∀ ch : Chain M, ch.head = ch.last → chainFlux L ch = 0 := Conserves.conserve
57
58end IndisputableMonolith