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Proof step 8 from proof copy-between (previous step)

0 < j, j0 < i0 + j, i0 ≤ j0, 0 < j, ∀ j1, r, r0, i0, j0, i, st. i→n(j1) < i→n(j) → (true → (r ≠ r0 ∧ i0 ≤ j0 ∧ j0 < i0 + j1 → (arraycopy(r, i, r0, i0, j1, st)[r0 -- j0 ']) = st[r -- ((j0 - i0) + i) '])) ⊦ (arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r0 -- j0 ']) = st[r -- (i + j0 - i0) '], r = r0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ i0 + j ≤ j0 → (arraycopy(r, i, r0, i0, j, st)[r0 -- j0 ']) = st[r0 -- j0 ']
Proof step 4:
¬ i0 + (j - 1) ≤ j0, 0 < j, j0 < i0 + j, i0 ≤ j0, 0 < j, ∀ j1, r, r0, i0, j0, i, st. i→n(j1) < i→n(j) → (true → (r ≠ r0 ∧ i0 ≤ j0 ∧ j0 < i0 + j1 → (arraycopy(r, i, r0, i0, j1, st)[r0 -- j0 ']) = st[r -- ((j0 - i0) + i) '])) ⊦ (arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r0 -- j0 ']) = st[r -- (i + j0 - i0) '], r = r0
Proof step 7:
i0 + (j - 1) ≤ j0, 0 < j, j0 < i0 + j, i0 ≤ j0, 0 < j, ∀ j1, r, r0, i0, j0, i, st. i→n(j1) < i→n(j) → (true → (r ≠ r0 ∧ i0 ≤ j0 ∧ j0 < i0 + j1 → (arraycopy(r, i, r0, i0, j1, st)[r0 -- j0 ']) = st[r -- ((j0 - i0) + i) '])) ⊦ (st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']][r0 -- j0 ']) = st[r -- (i + j0 - i0) '], r = r0

Rule argument

[crewrite-arg: copy-upper , F , [j0, st, j, i0, r0, i, r] → [j0, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']], j - 1, i0, r0, i, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (j0, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']], j - 1, i0, r0, i, r)]]