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Proof step 5 from proof copy-ident (previous step)

0 < j, ∀ j1, r, i, st, j0. i→n(j1) < i→n(j) → (true → (arraycopy(r, i, r, i, j1, st)[r -- j0 ']) = st[r -- j0 ']) ⊦ (arraycopy(r, i, r, i, j - 1, st[r -- (i + j - 1) ', st[r -- (i + j - 1) ']])[r -- j0 ']) = st[r -- j0 ']

User applied rule apply induction

And obtained the following new goals

Proof step 4:
(arraycopy(r, i, r, i, j - 1, st[r -- (i + j - 1) ', st[r -- (i + j - 1) ']])[r -- j0 ']) = (st[r -- (i + j - 1) ', st[r -- (i + j - 1) ']][r -- j0 ']), 0 < j, ∀ j1, r, i, st, j0. i→n(j1) < i→n(j) → (true → (arraycopy(r, i, r, i, j1, st)[r -- j0 ']) = st[r -- j0 ']) ⊦ (arraycopy(r, i, r, i, j - 1, st[r -- (i + j - 1) ', st[r -- (i + j - 1) ']])[r -- j0 ']) = st[r -- j0 ']

Rule argument

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

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, r, i, st[r -- (i + j - 1) ', st[r -- (i + j - 1) ']], j0)]]