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Proof step 13 from proof okbytearray-validref (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(byte_type)), r -- _type ∈ st, 0 ≤ i, r ∈ st, junkref(str, r, st), is_arrayref(r, i, st), r -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → is_bytevalue(st[r -- j ']) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(byte_type), st) ∧ (0 ≤ j ∧ j < i → 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 12:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(byte_type)), r -- _type ∈ st, 0 ≤ i, r ∈ st, junkref(str, r, st), is_arrayref(r, i, st), r -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → is_bytevalue(st[r -- j ']) ⊦ 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)) ∧ (0 ≤ j ∧ j < i → is_bytevalue(st[r -- j ']))

Rule argument

[speclemmaarg: , 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) ,[st, ty, val] → [st, mkarraytype(byte_type), refval(r)] ,F ,okfuns , ,okreftype ]

Additional information

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