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Proof step 11 from proof validrefs-primarray (previous step)

st[r -- _type] .type = mkarraytype(ty), st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, ty, st), r ∈ st, 0 ≤ i, 0 < st[r -- _length] .intval, is_primtype(ty), is_array(str, r, st), okarray(r, ty, st), i < st[r -- _length] .intval ⊦ r ' + r0 ' + refs = jvmref ', r = jvmref, is_reftype(ty)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 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 10:
st[r -- _type] .type = mkarraytype(ty), st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, ty, st), r ∈ st, 0 ≤ i, 0 < st[r -- _length] .intval, is_primtype(ty), is_array(str, r, 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)), i < st[r -- _length] .intval ⊦ r ' + r0 ' + refs = jvmref ', r = jvmref, is_reftype(ty)

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, ty, r] ,F ,okfuns , ,okarrayNotNull ]

Additional information

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