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Proof step 18 from proof copy-comp (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ i ≤ i0 ∧ i0 ≤ j0 ∧ j0 < i0 + j → (arraycopy(r, i, r, i0, j, st)[r -- j0 ']) = st[r -- ((j0 - i0) + i) ']
Proof step 15:
¬ (i1 ≤ i2 ∧ i2 ≤ i ∧ i < i2 + i3), st0[r2 -- _type] = typeval(mkarraytype(ty0)), st0[r2 -- _length] = intval(i0), i < i2 + i3, 0 ≤ i, i2 ≤ i, 0 ≤ i0, r2 -- _length ∈ st0, i2 + i3 ≤ i0, 0 ≤ i2, 0 ≤ i3, r2 -- _type ∈ st0, ty0 ≤ ty, r2 ∈ st0, i < i0, 0 < i2 + i3, i2 < i0, 0 < i0, 0 < i3, r2 -- i ' ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → r2 -- j ' ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i3 ≤ j → st0[r2 -- (i1 + j) '] = st0[r2 -- (i2 + j) '], ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st0[r2 -- j '], ty) ⊦ r2 = jvmref, (arraycopy(r2, i1, r2, i2, i3, st0)[r2 -- i ']) = st0[r2 -- i '], ¬ i1 ≤ i2 ∧ ¬ i2 + i3 ≤ i1
Proof step 17:
i1 ≤ i2 ∧ i2 ≤ i ∧ i < i2 + i3, st0[r2 -- _type] = typeval(mkarraytype(ty0)), st0[r2 -- _length] = intval(i0), i < i2 + i3, 0 ≤ i, i2 ≤ i, 0 ≤ i0, r2 -- _length ∈ st0, i2 + i3 ≤ i0, 0 ≤ i2, 0 ≤ i3, r2 -- _type ∈ st0, ty0 ≤ ty, r2 ∈ st0, i < i0, 0 < i2 + i3, i2 < i0, 0 < i0, 0 < i3, r2 -- i ' ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → r2 -- j ' ∈ st0, ∀ j. ¬ j < 0 ∧ ¬ i3 ≤ j → st0[r2 -- (i1 + j) '] = st0[r2 -- (i2 + j) '], ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st0[r2 -- j '], ty) ⊦ r2 = jvmref, st0[r2 -- ((i - i2) + i1) '] = st0[r2 -- i '], ¬ i1 ≤ i2 ∧ ¬ i2 + i3 ≤ i1

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i, st0, i3, i2, i1, r2)]]