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Proof step 9 from proof copy-in-lower (previous step)

0 < j, j0 < i0, ∀ j1, j0, i0, r0, r, i, st. i→n(j1) < i→n(j) → (true → (j0 < i0 → (r0 -- j0 ' ∈ 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i0 ≤ j0 ∧ j0 < i0 + j → r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j, st)
Proof step 8:
¬ (i0 ≤ j0 ∧ j0 < i0 + (j - 1)), 0 < j, j0 < i0, ∀ j1, j0, i0, r0, r, i, st. i→n(j1) < i→n(j) → (true → (j0 < i0 → (r0 -- j0 ' ∈ 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

Rule argument

[crewrite-arg: copy-in-between , 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 → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']], j - 1, i0, i, r, j0, r0)]]