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Proof step 23 from proof copy-succ (previous step)

0 ≤ j ⊦ r0 -- i ' ∈ (arraycopy(r1, i1, r0, i0, j, st)[r0 -- (i0 + j) ', st[r1 -- (i1 + j) ']]) ↔ r0 -- i ' ∈ arraycopy(r1, i1, r0, i0, j, st[r0 -- (i0 + j) ', st[r1 -- (i1 + j) ']]), r1 = r0, ¬ i < i0 ∧ ¬ i0 + j ≤ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ j0 < i0 → (r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j, st) ↔ r0 -- j0 ' ∈ st)
Proof step 20:
⊦ r0 -- (i0 + j) ' ∈ arraycopy(r, i, r0, i0, j, st) ↔ r0 -- (i0 + j) ' ∈ st
Proof step 21:
⊦ i0 + j ≤ j0 → (r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j, st) ↔ r0 -- j0 ' ∈ st)
Proof step 22:
⊦ j0 < i0 → (r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j, st) ↔ r0 -- j0 ' ∈ st)

Rule argument

[crewrite-arg: copy-in-lower , F , [st, j, i0, i, r, j0, r0] → [st[r0 -- (i0 + j) ', st[r1 -- (i1 + j) ']], j, i0, i1, r1, i, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i ≤ i], [CSIMPSEQ : ⊦ i + j ≤ i + j0 ↔ j ≤ j0], [CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPSEQ : ⊦ i ≤ i + j ↔ 0 ≤ j], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st])], [EXTRATERMS : (st[r0 -- (i0 + j) ', st[r1 -- (i1 + j) ']], j, i0, i1, r1, i, r0)]]