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Proof step 90 from proof validrefs-lastelem (previous step)

st[r0 -- i '] = refval(jvmref), st[r0 -- _type] = typeval(mkarraytype(ty0)), r0 -- _type ∈ st, okarray(r0, ty0, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, is_array(str, r0, st), mkarraytype(ty0) ≤ ty, i < st[r0 -- _length] .intval, r0 ∈ st ⊦ ty0 = void_type, r0 = jvmref, is_reftype(ty0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 85:
⊦ 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 89:
st[r0 -- i '] = refval(jvmref), st[r0 -- _type] = typeval(mkarraytype(ty0)), r0 -- _type ∈ st, okreftype(refval(r0), mkarraytype(ty0), st) ∧ r0 ≠ jvmref ∧ r0 -- _length ∈ st ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r0 -- _length] .intval → oktype(st[r0 -- j '], ty0, st)), 0 ≤ i, 0 < st[r0 -- _length] .intval, is_array(str, r0, st), mkarraytype(ty0) ≤ ty, i < st[r0 -- _length] .intval, r0 ∈ st ⊦ ty0 = void_type, r0 = jvmref, is_reftype(ty0)

Rule argument

[speclemmaarg: , 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)) ,[st, ty, r] → [st, ty0, r0] ,F ,okfuns , ,okarrayNotNull ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty0, r0)]]