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Proof step 9 from proof isarray-notin-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 8:
st[r -- _type] = typeval(mkarraytype(ty)), st[r -- _length] = intval(i0), 0 < i0, 0 ≤ i0, r -- _length ∈ st, ∀ j. 0 ≤ j ∧ j < i0 → r -- j ' ∈ st, i < i0, 0 ≤ i, r ∈ st, r -- _type ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, r -- i ' ∈ st

Rule argument

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

Additional information

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