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Proof step 11 from proof copy-bet-low (previous step)

2 * i0 + j = (i + (2 * i0 + j - i + 1)) + 1, (arraycopy(r, i, r, i0, j - 1, st[r -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r -- (2 * i0 + j - i + 1) ']) = st[r -- (i + j - 1) '], i ≤ 2 * i0 + j - i + 1, 2 * i0 + j - i + 1 < i0 + j, i0 ≤ 2 * i0 + j - i + 1, 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 + (2 * i0 + j - i + 1) - i0) ']

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ (arraycopy(r, i, r, i, j, st)[r -- j0 ']) = st[r -- j0 ']
Proof step 10:
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 -- (i0 + j - 1) '] = st[r -- (2 * i0 + j - 1 + i0) ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ i], [CSIMPSEQ : ⊦ i * 0 = 0], [CSIMPSEQ : ⊦ ((* i2)) * i < ((* i1)) * i + j0 ↔ (i2 - i1) * i < j0], [CSIMPSEQ : ⊦ i < i + j ↔ 0 < j], [CSIMPSEQ : ⊦ i - j = i0 ↔ i = i0 + j], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ i + j ≤ ((* i1)) * i + j0 ↔ j ≤ (i1 - 1) * i + j0], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ 1 * i = i], [CSIMPSEQ : ⊦ ((* i2)) * i < i + j0 ↔ (i2 - 1) * i < j0], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPSEQ : ⊦ i - j < i0 ↔ i < j + i0], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ i + i = 2 * i], [CSIMPSEQ : ⊦ i ≤ j - i0 ↔ i + i0 ≤ j], [CSIMPSEQ : ⊦ i - j - i0 = i - j + i0], [CSIMPSEQ : ⊦ i + j - i + 1 = j - 1], [CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0], [CSIMPSEQ : ⊦ i + j = i + i0 ↔ j = i0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + (j - i) = j], [CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ i + j = j + i])]]