`post_monotone`

proved

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module: IndisputableMonolith.LedgerPostingAdjacency
domain: LedgerPostingAdjacency
line: 664 · github
papers citing: none yet

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IndisputableMonolith.LedgerPostingAdjacency on GitHub at line 664.

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 661
 662/-! ### Posting steps satisfy `LegalAtomicTick` (and conversely, by `legalAtomicTick_implies_PostingStep`) -/
 663
 664private lemma post_monotone {d : Nat} (L : LedgerState d) (k : Fin d) (side : Side) :
 665    MonotoneLedger (d := d) L (post L k side) := by
 666  classical
 667  cases side with
 668  | debit =>
 669      refine ⟨?_, ?_⟩
 670      · intro i
 671        by_cases hik : i = k
 672        · subst hik
 673          simp [post]
 674        · simp [post, hik]
 675      · intro i
 676        simp [post]
 677  | credit =>
 678      refine ⟨?_, ?_⟩
 679      · intro i
 680        simp [post]
 681      · intro i
 682        by_cases hik : i = k
 683        · subst hik
 684          simp [post]
 685        · simp [post, hik]
 686
 687private lemma ledgerL1Cost_post {d : Nat} (L : LedgerState d) (k : Fin d) (side : Side) :
 688    ledgerL1Cost (d := d) L (post L k side) = 1 := by
 689  classical
 690  cases side with
 691  | debit =>
 692      -- debit changes by +1 at k; credit unchanged
 693      have hdebit :
 694          (∑ i : Fin d, Int.natAbs ((post L k Side.debit).debit i - L.debit i)) = 1 := by

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