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Proof step 15 from proof copy-bet-up (previous step)

j0 < i0 + j, i0 ≤ j0, i0 + j ≤ i, j0 < i, i0 < i, 0 < j, ∀ 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, st)[r -- j0 ']) = st[r -- (i + j0 - i0) ']

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 0 < j → arraycopy(r1, i1, r2, i2, j, st) = arraycopy(r1, i1, r2, i2, j - 1, st[r2 -- (i2 + j - 1) ', st[r1 -- (i1 + j - 1) ']])
Proof step 14:
0 < j, j0 < i0 + j, i0 ≤ j0, i0 + j ≤ i, j0 < i, i0 < i, 0 < j, ∀ 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 -- j0 ']) = st[r -- (i + j0 - i0) ']

Rule argument

[crewrite-arg: arrayCopy-rec , F , [st, j, i2, r2, i1, r1] → [st, j, i0, r, i, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, j, i0, r, i, r)]]