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Proof step 4 from proof copy-in (previous step)

0 < j, ∀ j0, r1, i, r, i1, r0, i0, st. i→n(j0) < i→n(j) → (true → (r1 -- i ' ∈ arraycopy(r, i1, r0, i0, j0, st) ↔ r1 -- i ' ∈ st) ∨ r1 = r0) ⊦ r1 = r0, r1 -- i ' ∈ arraycopy(r, i1, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i1 + j - 1) ']]) ↔ r1 -- i ' ∈ st

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [j0, r1, i, r, i1, r0, i0, st] → [j - 1, r1, i, r, i1, r0, i0, st[r0 -- (i0 + j - 1) ', st[r -- (i1 + j - 1) ']]] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( r -- sk ∈ st[r0 -- sk0, val] ↔ r -- sk ∈ st)], [CSIMPSEQ : ⊦ i→n(i - 1) < i→n(i) ↔ 0 < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (j - 1, r1, i, r, i1, r0, i0, st[r0 -- (i0 + j - 1) ', st[r -- (i1 + j - 1) ']])]]