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Proof step 19 from proof okbytearray-put-field (previous step)

okreftype(refval(r0), mkarraytype(byte_type), st[r0 -- fs ', val]) ∧ r0 ≠ jvmref ∧ r0 -- _length ∈ st[r0 -- fs ', val] ∧ is_integervalue(st[r0 -- fs ', val][r0 -- _length]) ∧ 0 ≤ (st[r0 -- fs ', val][r0 -- _length]) .intval ∧ is_arrayref(r0, (st[r0 -- fs ', val][r0 -- _length]) .intval, st[r0 -- fs ', val]) ∧ (∀ j. 0 ≤ j ∧ j < (st[r0 -- fs ', val][r0 -- _length]) .intval → oktype(st[r0 -- fs ', val][r0 -- j '], byte_type, st[r0 -- fs ', val])) ⊦ r0 = jvmref, fs ' = _type, fs ' = _length, okreftype(refval(r0), mkarraytype(byte_type), st) ∧ r0 -- _length ∈ st ∧ is_integervalue(st[r0 -- _length]) ∧ ¬ st[r0 -- _length] .intval < 0 ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ (0 ≤ j ∧ j < st[r0 -- _length] .intval → is_bytevalue(st[r0 -- j ']))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
⊦ okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty)
Proof step 10:
⊦ oktype(val, byte_type, st) ↔ is_bytevalue(val)
Proof step 18:
st[r0 -- _type] .type = mkarraytype(byte_type), r0 -- _type ∈ st, is_typevalue(st[r0 -- _type]), r0 -- _length ∈ st, is_integervalue(st[r0 -- _length]), is_arrayref(r0, st[r0 -- _length] .intval, st), r0 ∈ st, 0 ≤ st[r0 -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j0 → is_bytevalue(st[r0 -- j0 ']) ⊦ fs ' = _type, fs ' = _length, r0 = jvmref, okreftype(refval(r0), mkarraytype(byte_type), st) ∧ (0 ≤ j ∧ j < st[r0 -- _length] .intval → is_bytevalue(st[r0 -- j ']))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ (st[r0 -- fs ', val][r -- i ']) = st[r -- i ']], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ is_arrayref (r, i, st[r0 -- fs ', val]) ↔ is_arrayref(r, i, st)], [CSIMPSEQ : ⊦ ty ≤ mkarraytype(byte_type) ↔ ty = mkarraytype(byte_type)], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]