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Proof step 14 from proof exactarray-put-02 (previous step)

st[r -- _type] = typeval(mkarraytype(byte_type)), st[r -- _length] = intval(st[r -- _length] .intval), r -- _type ∈ st, r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), r ∈ st ⊦ r = jvmref, is_arrayref(r, st[r -- _length] .intval, st[r0 -- j ', byteval(by)])

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 13:
st[r -- _type] = typeval(mkarraytype(byte_type)), st[r -- _length] = intval(st[r -- _length] .intval), r -- _type ∈ st, r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), r ∈ st ⊦ r = jvmref, ∀ j0. 0 ≤ j0 ∧ j0 < st[r -- _length] .intval → r -- j0 ' ∈ st[r0 -- j ', byteval(by)]

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- j ', byteval(by)], st[r -- _length] .intval, r)]]