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Proof step 13 from proof okarray-copy-01 (previous step)

okarray(r0, byte_type, st), okarray(r, byte_type, st), 0 ≤ i, r0 ∈ st, r ∈ st, i + i1 < st[r0 -- _length] .intval, 0 ≤ i1, ∀ i0, i, r0, st, r, j0. i→n(j0) < i→n(i1 + 1) → ( okarray(r, byte_type, st) ∧ okarray(r0, byte_type, st) ∧ i + j0 ≤ st[r0 -- _length] .intval ∧ r ∈ st ∧ r0 ∈ st ∧ 0 ≤ i ∧ 0 ≤ j0 → r = jvmref ∨ r0 = jvmref ∨ okarray(r, byte_type, arraycopy(r0, i, r, i0, j0, st))) ⊦ r0 = jvmref, r = jvmref, okarray(r, byte_type, arraycopy(r0, i, r, i0, i1, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']])), is_bytevalue(st[r0 -- (i + i1) ']), okarray(r, byte_type, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']]) ∧ okarray(r0, byte_type, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))
Proof step 12:
okreftype(refval(r0), mkarraytype(byte_type), st) ∧ r0 ≠ jvmref ∧ r0 -- _length ∈ st ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r0 -- _length] .intval → oktype(st[r0 -- j '], byte_type, st)), okarray(r, byte_type, st), 0 ≤ i, r0 ∈ st, r ∈ st, i + i1 < st[r0 -- _length] .intval, 0 ≤ i1, ∀ i0, i, r0, st, r, j0. i→n(j0) < i→n(i1 + 1) → ( okarray(r, byte_type, st) ∧ okarray(r0, byte_type, st) ∧ i + j0 ≤ st[r0 -- _length] .intval ∧ r ∈ st ∧ r0 ∈ st ∧ 0 ≤ i ∧ 0 ≤ j0 → r = jvmref ∨ r0 = jvmref ∨ okarray(r, byte_type, arraycopy(r0, i, r, i0, j0, st))) ⊦ r0 = jvmref, r = jvmref, okarray(r, byte_type, arraycopy(r0, i, r, i0, i1, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']])), is_bytevalue(st[r0 -- (i + i1) ']), okarray(r, byte_type, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']]) ∧ okarray(r0, byte_type, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']])

Rule argument

[crewrite-arg: okarrayNotNull, F, [st, ty, r] → [st, byte_type, r0]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, byte_type, r0)]]