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Proof step 4 from proof copy-in-02 (previous step)

r ∈ st, ∀ j0, r, st, r1, i1, r2, i2. i→n(j0) < i→n(j) → (r ∈ st → r ∈ arraycopy(r1, i1, r2, i2, j0, st)) ⊦ r ∈ arraycopy(r1, i1, r2, i2, j, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 0 < j → arraycopy(r1, i1, r2, i2, j, st) = arraycopy(r1, i1, r2, i2, j - 1, st[r2 -- (i2 + j - 1) ', st[r1 -- (i1 + j - 1) ']])
Proof step 2:
⊦ j ≤ 0 → arraycopy(r1, i1, r2, i2, j, st) = st
Proof step 3:
0 < j, r ∈ st, ∀ j0, r, st, r1, i1, r2, i2. i→n(j0) < i→n(j) → (r ∈ st → r ∈ arraycopy(r1, i1, r2, i2, j0, st)) ⊦ r ∈ arraycopy(r1, i1, r2, i2, j - 1, st[r2 -- (i2 + j - 1) ', st[r1 -- (i1 + j - 1) ']])

Rule argument

[crewrite-arg: arrayCopy-rec , F , [st, j, i2, r2, i1, r1] → [st, j, i2, r2, i1, r1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPFORWARD : ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0])], [EXTRATERMS : (st, j, i2, r2, i1, r1)]]