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Proof step 22 from proof okarray-putbar-same-03 (previous step)

st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(byte_type)), r -- _length ∈ st, is_arrayref(r, i0, st), r -- _type ∈ st, r ∈ st, 0 ≤ i0, ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → is_bytevalue(st[r -- j0 ']) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(byte_type), putByteArray(bytes, r, i, st)) ∧ is_arrayref(r, i0, putByteArray(bytes, r, i, st)) ∧ (0 ≤ j ∧ j < i0 → is_bytevalue(putByteArray(bytes, r, i, st)[r -- j ']))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty)
Proof step 21:
st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(byte_type)), r -- _length ∈ st, is_arrayref(r, i0, st), r -- _type ∈ st, r ∈ st, 0 ≤ i0, ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → is_bytevalue(st[r -- j0 ']) ⊦ r = jvmref, is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ putByteArray(bytes, r, i, st) ∧ is_typevalue(putByteArray(bytes, r, i, st)[refval(r) .refval -- _type]) ∧ (putByteArray(bytes, r, i, st)[refval(r) .refval -- _type]) .type ≤ mkarraytype(byte_type)) ∧ is_arrayref(r, i0, putByteArray(bytes, r, i, st)) ∧ (0 ≤ j ∧ j < i0 → is_bytevalue(putByteArray(bytes, r, i, st)[r -- j ']))

Rule argument

[crewrite-arg: okreftype , F , [st, ty, val] → [putByteArray(bytes, r, i, st), mkarraytype(byte_type), refval(r)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (putByteArray(bytes, r, i, st), mkarraytype(byte_type), refval(r))]]