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Proof step 14 from proof isarray-putbar (previous step)

st[r1 -- _type] = typeval(mkarraytype(byte_type)), st[r1 -- _length] = intval(i0), 0 ≤ i0, r1 -- _length ∈ st, is_arrayref(r1, i0, st), is_array(r1, putByteArray(bytes0, r1, i + 1, st)[r1 -- i ', byteval(by)]), r1 -- _type ∈ st, r1 ∈ st, ∀ r1, i, st. is_array(r1, putByteArray(bytes0, r1, i, st)) ∧ okbytearray(r1, st) → is_array(r1, st), ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_bytevalue(st[r1 -- j ']) ⊦ r1 = jvmref, okreftype(refval(r1), mkarraytype(byte_type), st) ∧ (0 ≤ j ∧ j < i0 → is_bytevalue(st[r1 -- j ']))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 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 13:
st[r1 -- _type] = typeval(mkarraytype(byte_type)), st[r1 -- _length] = intval(i0), 0 ≤ i0, r1 -- _length ∈ st, is_arrayref(r1, i0, st), is_array(r1, putByteArray(bytes0, r1, i + 1, st)[r1 -- i ', byteval(by)]), r1 -- _type ∈ st, r1 ∈ st, ∀ r1, i, st. is_array(r1, putByteArray(bytes0, r1, i, st)) ∧ okbytearray(r1, st) → is_array(r1, st), ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_bytevalue(st[r1 -- j ']) ⊦ r1 = jvmref, is_referencevalue(refval(r1)) ∧ ( refval(r1) .refval ≠ jvmref → refval(r1) .refval -- _type ∈ st ∧ is_typevalue(st[refval(r1) .refval -- _type]) ∧ st[refval(r1) .refval -- _type] .type ≤ mkarraytype(byte_type)) ∧ (0 ≤ j ∧ j < i0 → is_bytevalue(st[r1 -- j ']))

Rule argument

[crewrite-arg: okreftype , F , [st, ty, val] → [st, mkarraytype(byte_type), refval(r1)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, mkarraytype(byte_type), refval(r1))]]