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Proof step 10 from proof isarray-abstract (previous step)

st[r -- _type] = typeval(mkarraytype(abstract_type)), r -- _type ∈ st, okarray(r, abstract_type, st), r ∈ st ⊦ st[r -- _length] .intval = 0, r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ okarray(r, ty, st) ↔ okreftype(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) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))
Proof step 9:
st[r -- _type] = typeval(mkarraytype(abstract_type)), r -- _type ∈ st, okreftype(refval(r), mkarraytype(abstract_type), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], abstract_type, st)), r ∈ st ⊦ st[r -- _length] .intval = 0, r = jvmref

Rule argument

[crewrite-arg: okarrayNotNull , F , [st, ty, r] → [st, abstract_type, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, abstract_type, r)]]