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Proof step 13 from proof copy-bet-up (previous step)

i0 + (j - 1) ≤ i ∧ i0 ≤ j0 ∧ j0 < i0 + (j - 1) → (arraycopy(r, i, r, i0, j - 1, st[r -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r -- j0 ']) = (st[r -- (i0 + j - 1) ', st[r -- (i + j - 1) ']][r -- ((j0 - i0) + i) ']), 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) ']

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
j0 < i0 + j, i0 ≤ j0, i0 + j ≤ i, j0 < i, i0 < i, 0 < j, ¬ 1 + i < i0 + j ∧ i0 + j ≠ 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) '])), ∀ 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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + i = 2 * i], [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 → (j ≤ i + 1 ↔ j = i + 1)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j - i0 ↔ i + i0 < j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i - j ≤ i0 ↔ i ≤ j + i0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0], [CSIMPSEQ : ⊦ i + j = j + i])]]