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Proof step 85 from proof copy-comp (previous step)

st0[r2 -- _length] = intval(i0), st0[r2 -- _type] = typeval(mkarraytype(ty0)), r2 ∈ st0, ty0 ≤ ty, r2 -- _type ∈ st0, 0 ≤ i3, 0 ≤ i2, i2 + i3 ≤ i0, r2 -- _length ∈ st0, 0 ≤ i0, i2 ≤ i, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st0[r2 -- j '], ty), ∀ j. ¬ j < 0 ∧ ¬ i3 ≤ j → st0[r1 -- (i1 + j) '] = st0[r2 -- (i2 + j) '], ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → r2 -- j ' ∈ st0 ⊦ r2 = jvmref, (r2 -- i ' ∈ arraycopy(r1, i1, r2, i2, i3, st0) ↔ r2 -- i ' ∈ st0) ∧ (arraycopy(r1, i1, r2, i2, i3, st0)[r2 -- i ']) = st0[r2 -- i '], r1 ≠ r2 ∧ ¬ i2 + i3 ≤ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i0 + j ≤ j0 → (arraycopy(r, i, r0, i0, j, st)[r0 -- j0 ']) = st[r0 -- j0 ']
Proof step 84:
¬ i2 + i3 ≤ i, st0[r2 -- _length] = intval(i0), st0[r2 -- _type] = typeval(mkarraytype(ty0)), r2 ∈ st0, ty0 ≤ ty, r2 -- _type ∈ st0, 0 ≤ i3, 0 ≤ i2, i2 + i3 ≤ i0, r2 -- _length ∈ st0, 0 ≤ i0, i2 ≤ i, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st0[r2 -- j '], ty), ∀ j. ¬ j < 0 ∧ ¬ i3 ≤ j → st0[r1 -- (i1 + j) '] = st0[r2 -- (i2 + j) '], ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → r2 -- j ' ∈ st0 ⊦ r2 = jvmref, (r2 -- i ' ∈ arraycopy(r1, i1, r2, i2, i3, st0) ↔ r2 -- i ' ∈ st0) ∧ (arraycopy(r1, i1, r2, i2, i3, st0)[r2 -- i ']) = st0[r2 -- i '], r1 ≠ r2 ∧ ¬ i2 + i3 ≤ i

Rule argument

[speclemmaarg: , i0 + j ≤ j0 → (arraycopy(r, i, r0, i0, j, st)[r0 -- j0 ']) = st[r0 -- j0 '] ,[j0, st, j, i0, r0, i, r] → [i, st0, i3, i2, r2, i1, r1] ,F ,storearrays , ,copy-upper ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i0 + j ≤ j0 → ( r0 -- j0 ' ∈ arraycopy (r, i, r0, i0, j, st) ↔ r0 -- j0 ' ∈ st)])], [EXTRATERMS : (i, st0, i3, i2, r2, i1, r1)]]