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Proof step 16 from proof isarray-putbar (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 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 15:
st[r1 -- _length] = intval(i0), st[r1 -- _type] = typeval(mkarraytype(byte_type)), r1 ∈ st, r1 -- _type ∈ st, is_array(r1, putByteArray(bytes0, r1, i + 1, st)[r1 -- i ', byteval(by)]), is_arrayref(r1, i0, st), r1 -- _length ∈ st, 0 ≤ i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_bytevalue(st[r1 -- j ']), ∀ r1, i, st. is_array(r1, putByteArray(bytes0, r1, i, st)) ∧ okbytearray(r1, st) → is_array(r1, st) ⊦ r1 = jvmref, okreftype(refval(r1), mkarraytype(byte_type), st) ∧ r1 ≠ jvmref ∧ r1 -- _length ∈ st ∧ is_integervalue(st[r1 -- _length]) ∧ 0 ≤ st[r1 -- _length] .intval ∧ is_arrayref(r1, st[r1 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r1 -- _length] .intval → oktype(st[r1 -- j '], byte_type, st))

Rule argument

[crewrite-arg: okarrayNotNull, F, [st, ty, r] → [st, byte_type, r1]]

Additional information

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