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Proof step 30 from proof okbytearray-put-byteval-equiv (previous step)

st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(byte_type)), r -- _type ∈ st, r -- _length ∈ st, is_arrayref(r, i0, st[r -- i ', byteval(by)]), r ∈ st, 0 ≤ i0, i < 0 ∨ i0 ≤ i ∨ 0 ≤ i ∧ i < i0 ∧ r -- i ' ∈ st ∧ is_bytevalue(st[r -- i ']), ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_bytevalue(st[r -- i ', byteval(by)][r -- j ']) ⊦ r = jvmref, okarray(r, byte_type, st)

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 29:
st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(byte_type)), r -- _type ∈ st, r -- _length ∈ st, is_arrayref(r, i0, st[r -- i ', byteval(by)]), r ∈ st, 0 ≤ i0, i < 0 ∨ i0 ≤ i ∨ 0 ≤ i ∧ i < i0 ∧ r -- i ' ∈ st ∧ is_bytevalue(st[r -- i ']), ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_bytevalue(st[r -- i ', byteval(by)][r -- j ']) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(byte_type), 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 '], byte_type, st))

Rule argument

[crewrite-arg: okarrayNotNull, F, [st, ty, r] → [st, byte_type, r]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, byte_type, r)]]