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Proof step 6 from proof copy-in-between (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ i0 + j ≤ j0 → (r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j, st) ↔ r0 -- j0 ' ∈ st)
Proof step 5:
¬ i0 + (j - 1) ≤ j0, 0 < j, 0 < j, i0 ≤ j0, j0 < i0 + j, ∀ j1, j0, i0, r0, r, i, st. i→n(j1) < i→n(j) → (j0 < i0 + j1 ∧ i0 ≤ j0 ∧ 0 < j1 → r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j1, st)) ⊦ r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([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 → (j ≤ i + 1 ↔ j = i + 1)], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ i - j = i0 ↔ i = i0 + j])], [EXTRATERMS : (st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']], j - 1, i0, i, r, j0, r0)]]