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Proof step 10 from proof copy-bet-bet (previous step)

(arraycopy(r, i, r, i0, j - 1, st[r -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r -- j0 ']) = st[r -- (i + j - 2 + (i0 + j - 2 + j0) % (i - i0)) '], j0 < i0 + j, i0 ≤ j0, i < i0 + j, i0 < i, 0 < j, ∀ j1, i0, i, j0, r, st. i→n(j1) < i→n(j) → ( true → ( i0 < i ∧ i < i0 + j1 ∧ i0 ≤ j0 ∧ j0 < i0 + j1 → (arraycopy(r, i, r, i0, j1, st)[r -- j0 ']) = st[r -- (i + j1 - (i0 + j1 - j0 + 1) % (i - i0) + 1) '])) ⊦ st[r -- (i + j - 2 + (i0 + j - 2 + j0) % (i - i0)) '] = st[r -- (i + j - (i0 + j - j0 + 1) % (i - i0) + 1) '], i0 + j = j0 + 1, i0 + j = i + 1, i = 1 + i0 + (i0 + j - 2 + j0) % (i - i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ (i - 1) % j + 1 ≠ j ∧ 0 < i ∧ 0 < j → i % j = (i - 1) % j + 1

Rule argument

[speclemmaarg: ,(i - 1) % j + 1 ≠ j ∧ 0 < i ∧ 0 < j → i % j = (i - 1) % j + 1 ,[j, i] → [i - i0, i0 + j - j0 + 1] ,F ,int-div , ,mod-pred ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i - j - i0 = i - j + i0], [CSIMPSEQ : ⊦ i - j = i0 ↔ i = i0 + j], [CSIMPSEQ : ⊦ i < j - i0 ↔ i + i0 < j], [CSIMPSEQ : ⊦ i ≠ i0 → (¬ i < i0 ↔ i0 < i)], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (i - i0, i0 + j - j0 + 1)]]