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Proof step 11 from proof copy-lower (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ r ≠ r0 ∧ i0 ≤ j0 ∧ j0 < i0 + j → (arraycopy(r, i, r0, i0, j, st)[r0 -- j0 ']) = st[r -- ((j0 - i0) + i) ']
Proof step 10:
¬ (r ≠ r0 ∧ i0 ≤ j0 ∧ j0 < i0 + (j - 1)), 0 < j, j0 < i0, ∀ j1, j0, i0, r, i, r0, st. i→n(j1) < i→n(j) → (j0 < i0 → (arraycopy(r, i, r0, i0, j1, st)[r0 -- j0 ']) = st[r0 -- j0 ']) ⊦ (arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r0 -- j0 ']) = st[r0 -- j0 ']

Rule argument

[crewrite-arg: copy-between , 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 : ([CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (j0, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']], j - 1, i0, r0, i, r)]]