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Proof step 4 from proof copy-bet-up (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i0 + j ≤ j0 → (arraycopy(r, i, r0, i0, j, st)[r0 -- j0 ']) = st[r0 -- j0 ']

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i - j ≤ i0 ↔ i ≤ j + i0], [CSIMPSEQ : ⊦ i + (j - i) = j], [CSIMPSEQ : ⊦ i + j ≤ i + j0 ↔ j ≤ j0], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < i])], [EXTRATERMS : (i0 + j - 1, st[r -- (i0 + j - 1) ', st[r -- (i + j - 1) ']], j - 1, i0, r, i, r)]]