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Proof step 15 from proof isarray-keyin (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
st[r0 -- _length] = intval(i0), st[r0 -- _type] = typeval(mkarraytype(ty)), st[r -- sk] = refval(r0), 0 ≤ i0, r0 -- _type ∈ st, i < st[r -- (sk ' + _length ')] .intval, 0 ≤ i, 0 < st[r -- (sk ' + _length ')] .intval, r0 ∈ st, is_arrayref(r0, i0, st), is_integervalue(st[r0 -- _length]), r0 -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r0 -- j '], ty) ⊦ r0 = jvmref, r0 -- i ' ∈ st

Rule argument

[speclemmaarg: ,is_integervalue(val) → (i = val .intval ↔ val = intval(i)) ,[val, i] → [st[r0 -- _length], i0] ,T ,javavalue , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_integervalue(val) → ( i = val .intval ↔ val = intval(i))])], [EXTRATERMS : (st[r0 -- _length], i0)]]