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Proof step 51 from proof okarray-union-03 (previous step)

st[r -- _length] = intval(st[r -- _length] .intval), st[r -- _type] = typeval(mkarraytype(ty0)), r -- _length ∈ st, r -- _type ∈ st, r ∈ st, ty0 ≤ ty, is_arrayref(r, st[r -- _length] .intval, st), 0 ≤ st[r -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → oktype(st[r -- j0 '], ty, st) ⊦ is_arrayref(r, st[r -- _length] .intval, st0 ∪ st), r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 50:
st[r -- _length] = intval(st[r -- _length] .intval), st[r -- _type] = typeval(mkarraytype(ty0)), r -- _length ∈ st, r -- _type ∈ st, r ∈ st, ty0 ≤ ty, is_arrayref(r, st[r -- _length] .intval, st), 0 ≤ st[r -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → oktype(st[r -- j0 '], ty, st) ⊦ ∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → r -- j ' ∈ st0 ∪ st, r = jvmref

Rule argument

[speclemmaarg: ,is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st) ,[st, i, r] → [st0 ∪ st, st[r -- _length] .intval, r] ,F ,storearrays , ,is_arrayref ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0 ∪ st, st[r -- _length] .intval, r)]]