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Proof step 17 from proof subset-exactarray (previous step)

st[r -- _length] = intval(i), st0[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), r ∈ st0, r -- _length ∈ st0, 0 ≤ i, r ∈ st, r -- _type ∈ st, is_arrayref(r, i, st), r -- _length ∈ st, r -- _type ∈ st0, ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r = jvmref, is_arrayref(r, i, st0) ∧ exactreftype(refval(r), mkarraytype(ty), st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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 16:
st[r -- _length] = intval(i), st0[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), r ∈ st0, r -- _length ∈ st0, 0 ≤ i, r ∈ st, r -- _type ∈ st, is_arrayref(r, i, st), r -- _length ∈ st, r -- _type ∈ st0, ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r = jvmref, is_arrayref(r, i, st0) ∧ is_referencevalue(refval(r)) ∧ refval(r) .refval ∈ st0 ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st0 ∧ is_typevalue(st0[refval(r) .refval -- _type]) ∧ st0[refval(r) .refval -- _type] .type = mkarraytype(ty))

Rule argument

[crewrite-arg: exactreftype , F , [st, ty, val] → [st0, mkarraytype(ty), refval(r)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, mkarraytype(ty), refval(r))]]