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Proof step 31 from proof okbytearray (previous step)

0 < i0, 0 ≤ i, r ∈ st, i + i0 < st[r -- _length] .intval, okarray(r, byte_type, st), ∀ val, i, st, r, j0. i→n(j0) < i→n(i0 + 1) → (true → (okarray(r, byte_type, st) ∧ i + j0 ≤ st[r -- _length] .intval ∧ 0 ≤ i ∧ ¬ is_bytevalue(val) → ¬ val ∈ getarray(r, i, j0, st))) ⊦ r = jvmref, is_bytevalue(st[r -- (i + i0) ']), st[r -- (i + i0) '] ∈ getarray(r, i, i0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ 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 30:
0 < i0, 0 ≤ i, r ∈ st, i + i0 < st[r -- _length] .intval, okreftype(refval(r), mkarraytype(byte_type), 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 '], byte_type, st)), ∀ val, i, st, r, j0. i→n(j0) < i→n(i0 + 1) → (true → (okarray(r, byte_type, st) ∧ i + j0 ≤ st[r -- _length] .intval ∧ 0 ≤ i ∧ ¬ is_bytevalue(val) → ¬ val ∈ getarray(r, i, j0, st))) ⊦ r = jvmref, is_bytevalue(st[r -- (i + i0) ']), st[r -- (i + i0) '] ∈ getarray(r, i, i0, st)

Rule argument

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

Additional information

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