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Proof step 28 from proof okbytearray-put-byteval-equiv (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 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 27:
st[r -- _type] = typeval(mkarraytype(byte_type)), st[r -- _length] = intval(i0), 0 ≤ i0, r ∈ st, is_arrayref(r, i0, st[r -- i ', byteval(by)]), r -- _length ∈ st, r -- _type ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_bytevalue(st[r -- i ', byteval(by)][r -- j ']), i < 0 ∨ i0 ≤ i ∨ 0 ≤ i ∧ i < i0 ∧ r -- i ' ∈ st ∧ is_bytevalue(st[r -- i ']) ⊦ r = jvmref, is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st ∧ is_typevalue(st[refval(r) .refval -- _type]) ∧ st[refval(r) .refval -- _type] .type ≤ mkarraytype(byte_type)) ∧ is_arrayref(r, i0, st) ∧ (0 ≤ j ∧ j < i0 → is_bytevalue(st[r -- j ']))

Rule argument

[crewrite-arg: okreftype , F , [st, ty, val] → [st, mkarraytype(byte_type), refval(r)] ]

Additional information

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