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Proof step 13 from proof isarray-keyin (previous step)

st[r -- sk] = refval(r0), st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), 0 ≤ i0, r0 -- _length ∈ st, is_arrayref(r0, i0, st), r0 ∈ st, 0 < st[r -- (sk ' + _length ')] .intval, 0 ≤ i, i < st[r -- (sk ' + _length ')] .intval, r0 -- _type ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r0 -- j '], ty) ⊦ r0 = jvmref, r0 -- i ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 12:
st[r -- sk] = refval(r0), st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), 0 ≤ i0, r0 -- _length ∈ st, ∀ j. 0 ≤ j ∧ j < i0 → r0 -- j ' ∈ st, r0 ∈ st, 0 < st[r -- (sk ' + _length ')] .intval, 0 ≤ i, i < st[r -- (sk ' + _length ')] .intval, r0 -- _type ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r0 -- j '], ty) ⊦ r0 = jvmref, r0 -- i ' ∈ st

Rule argument

[speclemmaarg: ,is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st) ,[st, i, r] → [st, i0, r0] ,F ,storearrays , ,is_arrayref ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i0, r0)]]