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Proof step 11 from proof union-okarray (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 10:
st[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = intval(i), 0 ≤ i, r -- _length ∈ st, r -- _type ∈ st, ty0 ≤ ty, r ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r -- j ' ∈ st ⊦ r = jvmref, ∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st0 ∪ st

Rule argument

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

Additional information

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