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Proof step 7 from proof copy-in-lower (previous step)

j0 < i0, 0 < j, ∀ j1, j0, i0, r0, r, i, st. i→n(j1) < i→n(j) → (true → (j0 < i0 → (r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j1, st) ↔ r0 -- j0 ' ∈ st))) ⊦ r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']]) ↔ r0 -- j0 ' ∈ st

User applied rule apply induction

And obtained the following new goals

Proof step 6:
j0 < i0 → ( r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']]) ↔ r0 -- j0 ' ∈ st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']]), j0 < i0, 0 < j, ∀ j1, j0, i0, r0, r, i, st. i→n(j1) < i→n(j) → (true → (j0 < i0 → (r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j1, st) ↔ r0 -- j0 ' ∈ st))) ⊦ r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']]) ↔ r0 -- j0 ' ∈ st

Rule argument

[substlist-arg: [j1, j0, i0, r0, r, i, st] → [j - 1, j0, i0, r0, r, i, st[r0 -- (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, j0, i0, r0, r, i, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])]]