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Proof step 62 from proof okarray-union-03 (previous step)

st[r -- _length] = intval(st[r -- _length] .intval), r ∈ st, okarray(refval(r), ty, st[r -- _length] .intval, st), r -- _length ∈ st ⊦ r = jvmref, (0 ≤ j ∧ j < st[r -- _length] .intval → oktype((st0 ∪ st)[r -- j '], ty, st0 ∪ st)) ∧ is_arrayref(r, st[r -- _length] .intval, st0 ∪ st) ∧ ¬ st[r -- _length] .intval < 0 ∧ okreftype(refval(r), mkarraytype(ty), st0 ∪ st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty)
Proof step 61:
st[r -- _length] = intval(st[r -- _length] .intval), r ∈ st, okarray(refval(r), ty, st[r -- _length] .intval, st), r -- _length ∈ st ⊦ r = jvmref, (0 ≤ j ∧ j < st[r -- _length] .intval → oktype((st0 ∪ st)[r -- j '], ty, st0 ∪ st)) ∧ is_arrayref(r, st[r -- _length] .intval, st0 ∪ st) ∧ ¬ st[r -- _length] .intval < 0 ∧ is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st0 ∪ st ∧ is_typevalue((st0 ∪ st)[refval(r) .refval -- _type]) ∧ (st0 ∪ st)[refval(r) .refval -- _type] .type ≤ mkarraytype(ty))

Rule argument

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

Additional information

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