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Proof step 12 from proof okarray-06 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
st[r -- _length] = intval(i), newref(r0, st), r ∈ st, is_integervalue(st[r -- _length]), 0 ≤ i ⊦ r0 = 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 '])), r = jvmref

Rule argument

[speclemmaarg: ,is_integervalue(val) → (i = val .intval ↔ val = intval(i)) ,[val, i] → [st[r -- _length], i] ,T ,javavalue , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_integervalue(val) → ( i = val .intval ↔ val = intval(i))])], [EXTRATERMS : (st[r -- _length], i)]]