`post`

definition

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module: IndisputableMonolith.LedgerPostingAdjacency
domain: LedgerPostingAdjacency
line: 74 · github
papers citing: none yet

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IndisputableMonolith.LedgerPostingAdjacency on GitHub at line 74.

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formal source

  71deriving DecidableEq, Repr
  72
  73/-- Apply a single unit post (either debit or credit) at account `k`. -/
  74noncomputable def post {d : Nat} (L : LedgerState d) (k : Fin d) (side : Side) : LedgerState d := by
  75  classical
  76  exact match side with
  77  | Side.debit =>
  78      { debit := fun i => if i = k then L.debit i + 1 else L.debit i
  79      , credit := L.credit }
  80  | Side.credit =>
  81      { debit := L.debit
  82      , credit := fun i => if i = k then L.credit i + 1 else L.credit i }
  83
  84@[simp] lemma phiVec_post_debit {d : Nat} (L : LedgerState d) (k : Fin d) (i : Fin d) :
  85    phiVec (d := d) (post L k Side.debit) i =
  86      (if i = k then phiVec (d := d) L i + 1 else phiVec (d := d) L i) := by
  87  by_cases hik : i = k
  88  · subst hik
  89    simp [post, phiVec, Recognition.phi]
  90    ring_nf
  91  · simp [post, phiVec, Recognition.phi, hik]
  92
  93@[simp] lemma phiVec_post_credit {d : Nat} (L : LedgerState d) (k : Fin d) (i : Fin d) :
  94    phiVec (d := d) (post L k Side.credit) i =
  95      (if i = k then phiVec (d := d) L i - 1 else phiVec (d := d) L i) := by
  96  by_cases hik : i = k
  97  · subst hik
  98    simp [post, phiVec, Recognition.phi]
  99    ring_nf
 100  · simp [post, phiVec, Recognition.phi, hik]
 101
 102/-! ## Bridge: a post induces a coord-atomic step on `phi` -/
 103
 104lemma phiVec_coordAtomicStep_of_post {d : Nat} (L : LedgerState d) (k : Fin d) (side : Side) :

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