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Proof step 31 from proof okarray-substore (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 30:
st[r -- _length] = intval(i), st0[r -- _length] = intval(i), st0[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _type] = typeval(mkarraytype(ty0)), r -- _length ∈ st0, is_arrayref(r, i, st), r -- _type ∈ st, ty0 ≤ ty, r -- _length ∈ st, 0 ≤ i, r ∈ st, r -- _type ∈ st0, r ∈ st0, ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st), ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ ∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st0, r = jvmref

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, i, r)]]