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Proof step 20 from proof okbytearray-put-field (previous step)

okarray(r0, 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 ']))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))
Proof step 19:
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 ']))

Rule argument

[crewrite-arg: okarrayNotNull , F , [st, ty, r] → [st[r0 -- fs ', val], byte_type, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- fs ', val], byte_type, r0)]]