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Proof step 13 from proof copy-bet-low (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 ']) = st[r -- (i + j - 1) '], i ≤ j0, j0 < i0 + j, i0 ≤ j0, i ≤ i0, i < i0 + j, 0 < j, ∀ j1, i, i0, j0, r, st. i→n(j1) < i→n(j) → (true → (i ≤ i0 ∧ 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) ']

User applied rule cut formula

And obtained the following new goals

Proof step 12:
j0 = 2 * i0 + j - i + 1, 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) '], i ≤ j0, j0 < i0 + j, i0 ≤ j0, i ≤ i0, i < i0 + j, 0 < j, ∀ j1, i, i0, j0, r, st. i→n(j1) < i→n(j) → (true → (i ≤ i0 ∧ 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

[fma-arg: j0 = 2 * i0 + j - i + 1]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ i - j = i0 ↔ i = i0 + j])], [EXTRAFMAS : (j0 = 2 * i0 + j - i + 1)]]