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Proof step 22 from proof okarray-putbar-01 (previous step)

st[r -- _type] = typeval(mkarraytype(byte_type)), st[r -- _length] = intval(i), 0 ≤ i, r ∈ st, is_arrayref(r, i, putByteArray(bytes, r1, 0, st)), r -- _length ∈ st, r -- _type ∈ st, r ∈ putByteArray(bytes, r1, 0, st), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → is_bytevalue(st[r -- j ']) ⊦ r = jvmref, r = r1, okreftype(refval(r), mkarraytype(byte_type), st) ∧ is_arrayref(r, i, st) ∧ (0 ≤ j ∧ j < i → is_bytevalue(st[r -- j ']))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 21:
st[r -- _type] = typeval(mkarraytype(byte_type)), st[r -- _length] = intval(i), 0 ≤ i, r ∈ st, ∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ putByteArray(bytes, r1, 0, st), r -- _length ∈ st, r -- _type ∈ st, r ∈ putByteArray(bytes, r1, 0, st), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → is_bytevalue(st[r -- j ']) ⊦ r = jvmref, r = r1, okreftype(refval(r), mkarraytype(byte_type), st) ∧ is_arrayref(r, i, st) ∧ (0 ≤ j ∧ j < i → is_bytevalue(st[r -- j ']))

Rule argument

[speclemmaarg: ,is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st) ,[st, i, r] → [putByteArray(bytes, r1, 0, st), i, r] ,F ,storearrays , ,is_arrayref ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (putByteArray(bytes, r1, 0, st), i, r)]]