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Proof step 14 from proof exactarray-08 (previous step)

st[r -- _type] = typeval(mkarraytype(int_type)), st[r -- _length] = intval(i), 0 ≤ i, r ∈ st, r -- _type ∈ st, is_integervalue(val), is_arrayref(r, i, st), r -- _length ∈ st ⊦ r = jvmref, exactreftype(refval(r), mkarraytype(int_type), st[r0 -- j ', val]) ∧ is_arrayref(r, i, st[r0 -- j ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ exactreftype(val, ty, st) ↔ is_referencevalue(val) ∧ val .refval ∈ st ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type = ty)
Proof step 13:
st[r -- _type] = typeval(mkarraytype(int_type)), st[r -- _length] = intval(i), 0 ≤ i, r ∈ st, r -- _type ∈ st, is_integervalue(val), is_arrayref(r, i, st), r -- _length ∈ st ⊦ r = jvmref, is_referencevalue(refval(r)) ∧ refval(r) .refval ∈ st[r0 -- j ', val] ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st[r0 -- j ', val] ∧ is_typevalue(st[r0 -- j ', val][refval(r) .refval -- _type]) ∧ (st[r0 -- j ', val][refval(r) .refval -- _type]) .type = mkarraytype(int_type)) ∧ is_arrayref(r, i, st[r0 -- j ', val])

Rule argument

[crewrite-arg: exactreftype , F , [st, ty, val] → [st[r0 -- j ', val], mkarraytype(int_type), refval(r)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- j ', val], mkarraytype(int_type), refval(r))]]