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Proof step 17 from proof subset-len-01 (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), r -- _length ∈ st, is_arrayref(r, i, st), st ⊆ st0, r ∈ st0, exactarray(r, ty, st0), r -- _type ∈ st, r ∈ st, 0 ≤ i ⊦ st0[r -- _length] .intval = i, r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ exactarray(r, ty, st) ↔ exactreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st)
Proof step 16:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), r -- _length ∈ st, is_arrayref(r, i, st), st ⊆ st0, r ∈ st0, exactreftype(refval(r), mkarraytype(ty), st0) ∧ r ≠ jvmref ∧ r -- _length ∈ st0 ∧ is_integervalue(st0[r -- _length]) ∧ 0 ≤ st0[r -- _length] .intval ∧ is_arrayref(r, st0[r -- _length] .intval, st0), r -- _type ∈ st, r ∈ st, 0 ≤ i ⊦ st0[r -- _length] .intval = i, r = jvmref

Rule argument

[crewrite-arg: exactarray-02, F, [st, ty, r] → [st0, ty, r]]

Additional information

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