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Proof step 32 from proof isarray-update (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 31:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), is_arrayref(r, i, st), r -- _type ∈ st, r ∈ st, r -- _length ∈ st, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, r = r0, ∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ update(r0, fis, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (update(r0, fis, st), i, r)]]