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Proof step 19 from proof copy-bet-low (previous step)

0 < j, 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) '])) ⊦ (arraycopy(r, i, r, i0, j - 1, st[r -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r -- j0 ']) = st[r -- (i + j0 - i0) ']

User applied rule apply induction

And obtained the following new goals

Proof step 18:
i ≤ i0 ∧ 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, 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) '])) ⊦ (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

[substlist-arg: [j1, i, i0, j0, r, st] → [j - 1, i, i0, j0, r, st[r -- (i0 + j - 1) ', st[r -- (i + j - 1) ']]] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i→n(i - 1) < i→n(i) ↔ 0 < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (j - 1, i, i0, j0, r, st[r -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])]]