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Proof step 9 from proof okarray-06 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ r ≠ r0 → (r -- sk ∈ addarray(r0, ty, vals, st) ↔ r -- sk ∈ st)
Proof step 7:
⊦ r ≠ r0 → (is_arrayref(r, i, addarray(r0, ty0, vals, st)) ↔ is_arrayref(r, i, st))
Proof step 8:
st[r -- _length] = intval(i), 0 ≤ i, newref(r0, st), j < i, r -- _length ∈ st, is_arrayref(r, i, st), okreftype(refval(r), mkarraytype(byte_type), st), 0 ≤ j, 0 < i, r ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → is_bytevalue(st[r -- j ']) ⊦ r0 = jvmref, r = jvmref, is_bytevalue(st[r -- j '])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ newref(r, st) ∧ r0 ∈ st → r ≠ r0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]