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Proof step 10 from proof okarray-06 (previous step)

st[r -- _length] = intval(i), 0 ≤ i, r ∈ st, newref(r0, st) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(byte_type), addarray(r0, ty, vals, st)) ∧ r -- _length ∈ addarray(r0, ty, vals, st) ∧ is_arrayref(r, i, addarray(r0, ty, vals, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → is_bytevalue(st[r -- j '])) ↔ okreftype(refval(r), mkarraytype(byte_type), st) ∧ r -- _length ∈ st ∧ is_arrayref(r, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → is_bytevalue(st[r -- j '])), r0 = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ r ≠ r0 → (okreftype(refval(r), ty, addarray(r0, ty0, vals, st)) ↔ okreftype(refval(r), ty, st))
Proof step 5:
⊦ r -- _length ∈ addarray(r, ty, vals, st)
Proof step 9:
r ≠ r0, st[r -- _length] = intval(i), 0 ≤ i, r ∈ st, newref(r0, st) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(byte_type), st) ∧ r -- _length ∈ addarray(r0, ty, vals, st) ∧ is_arrayref(r, i, addarray(r0, ty, vals, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → is_bytevalue(st[r -- j '])) ↔ okreftype(refval(r), mkarraytype(byte_type), st) ∧ r -- _length ∈ st ∧ is_arrayref(r, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → is_bytevalue(st[r -- j '])), r0 = jvmref

Rule argument

[crewrite-arg: okreftype-init , F , [st, vals, ty0, r0, ty, r] → [st, vals, ty, r0, mkarraytype(byte_type), r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ st → ¬ newref(r, st)])], [EXTRATERMS : (st, vals, ty, r0, mkarraytype(byte_type), r)]]