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Proof step 25 from proof okarray-copy (previous step)

st[r0 -- _length] = intval(i), 0 ≤ i, r0 ∈ st, is_arrayref(r0, i, st), r0 -- _length ∈ st, okreftype(refval(r0), mkarraytype(byte_type), st), ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → is_bytevalue(st[r0 -- j0 ']) ⊦ r0 = jvmref, r = jvmref, okreftype(refval(r), mkarraytype(byte_type), arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))) ∧ is_arrayref(r, i, arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))) ∧ (0 ≤ j ∧ j < i → is_bytevalue(arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))[r -- j ']))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 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 24:
st[r0 -- _length] = intval(i), 0 ≤ i, r0 ∈ st, is_arrayref(r0, i, st), r0 -- _length ∈ st, okreftype(refval(r0), mkarraytype(byte_type), st), ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → is_bytevalue(st[r0 -- j0 ']) ⊦ r0 = jvmref, r = jvmref, is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st)) ∧ is_typevalue(arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))[refval(r) .refval -- _type]) ∧ (arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))[refval(r) .refval -- _type]) .type ≤ mkarraytype(byte_type)) ∧ is_arrayref(r, i, arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st))) ∧ (0 ≤ j ∧ j < i → is_bytevalue(arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, 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] → [arraycopy(r0, 0, r, 0, i, addarray(r, byte_type, i, st)), mkarraytype(byte_type), refval(r)] ,F ,okfuns , ,okreftype ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (arraycopy (r0, 0, r, 0, i, addarray(r, byte_type, i, st)), mkarraytype(byte_type), refval(r))]]