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Proof step 30 from proof copy-bet-bet (previous step)

i0 + j = i + 1, i0 < i, j0 < i, i0 ≤ j0, 0 < j, i0 ≤ i, ∀ 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) '])) ⊦ 2 * i0 + j = (i + j0) + 1, i = j0, st[r -- (i + j0 - i0) '] = st[r -- (i + j - 1 + (i - j0) % (i - i0)) ']

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ j = i0 + j0 ↔ j - j0 = i0
Proof step 29:
i0 + j - 1 = i, i0 < i, j0 < i, i0 ≤ j0, 0 < j, i0 ≤ i, ∀ 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) '])) ⊦ 2 * i0 + j = (i + j0) + 1, i = j0, st[r -- (i + j0 - i0) '] = st[r -- (i + j - 1 + (i - j0) % (i - i0)) ']

Rule argument

[speclemmaarg: ,((* j)) = i0 + ((* j0)) ↔ j - j0 = i0 ,[j0, i0, j] → [1, i, i0 + j] ,F ,int-abs , ,numadd-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (1, i, i0 + j)]]