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Proof step 7 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) '])) ⊦ ¬ 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 ']) = st[r -- (i + j0 - i0) ']

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
i0 + j = j0 + 1, i0 ≤ j0, j0 ≤ i, 0 < j, i0 < i, j0 < i, i0 ≤ i, ∀ 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 -- j0 ', st[r -- (i + j - 1) ']])[r -- j0 ']) = st[r -- (i + j0 - i0) ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1], [CSIMPSEQ : ⊦ i ≤ i], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ i + j ≤ i + j0 ↔ j ≤ j0], [CSIMPSEQ : ⊦ i < j + i0 ∧ j < j0 → i < j0 + i0], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPSEQ : ⊦ i + j = j + i])]]