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Proof step 58 from proof okarray-union-03 (previous step)

st[r -- _length] = intval(st[r -- _length] .intval), r -- _type ∈ st, 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 ∧ st[r -- _type] .type ≤ mkarraytype(ty)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ okarray(val, ty, i, st) ↔ okreftype(val, mkarraytype(ty), st) ∧ val .refval ≠ jvmref ∧ (val .refval -- _length) × intval(i) ∈ st ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st[val .refval -- j '], ty, st))
Proof step 57:
st[r -- _length] = intval(st[r -- _length] .intval), r -- _type ∈ st, r ∈ st, okreftype(refval(r), mkarraytype(ty), st) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(st[r -- _length] .intval) ∈ st ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(refval(r) .refval, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[refval(r) .refval -- j '], ty, 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 ∧ st[r -- _type] .type ≤ mkarraytype(ty)

Rule argument

[crewrite-arg: okarrayOfLength , F , [st, i, ty, val] → [st, st[r -- _length] .intval, ty, refval(r)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r -- _length] .intval, ty, refval(r))]]