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Proof step 28 from proof copy-bet-bet (previous step)

j0 + 1 < i0 + j, i0 < j0, 1 < j, 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) '])) ⊦ i0 = j0, i0 + j = j0 + 1, st[r -- (j0 + j - 1) '] = st[r -- (2 * j + i0 - 2 + (i0 + j - 1 + j0) % (j - 1)) ']

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ abs(i) < j → i % j = i
Proof step 27:
¬ abs(i0 + j - 1 + j0) < j - 1, j0 + 1 < i0 + j, i0 < j0, 1 < j, 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) '])) ⊦ i0 = j0, i0 + j = j0 + 1, st[r -- (j0 + j - 1) '] = st[r -- (2 * j + i0 - 2 + (i0 + j - 1 + j0) % (j - 1)) ']

Rule argument

[speclemmaarg: ,abs(i) < j → i % j = i ,[j, i] → [j - 1, i0 + j - 1 + j0] ,F ,int-div , ,mod-zero-05 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0], [CSIMPSEQ : ⊦ i - (j - j0) = i + j0 - j], [CSIMPSEQ : ⊦ 2 * i0 + j - i0 + j0 = i0 + j - j0], [CSIMPSEQ : ⊦ i + j - i0 + j = i - i0], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0], [CSIMPSEQ : i < 0 ⊦ ((* i)) + j = j - ~ i], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ i * j = j * i])], [EXTRATERMS : (j - 1, i0 + j - 1 + j0)]]