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Proof step 9 from proof copy-bet-up (previous step)

2 * i0 + j = (i + j0) + 1, (arraycopy(r, i, r, i0, j - 1, st[r -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r -- j0 ']) = ((2 * i0 + j = (i + j0) + 1 ⊃ st[r -- (i + j - 1) ']; st[r -- (i + j0 - i0) '])), 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) '])) ⊦ st[r -- (i + j - 1) '] = st[r -- (i + j0 - i0) ']

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
2 * i0 + j = (i + j0) + 1, (arraycopy(r, i, r, i0, j - 1, st[r -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r -- j0 ']) = st[r -- (i + j - 1) '], 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) '])) ⊦ st[r -- (i + j - 1) '] = st[r -- (i + j0 - i0) ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i])]]