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Proof step 8 from proof isarray-abstract (previous step)

st[r -- _type] = typeval(mkarraytype(abstract_type)), 0 < st[r -- _length] .intval, is_integervalue(st[r -- _length]), r -- _length ∈ st, r -- _type ∈ st, r ∈ st, is_arrayref(r, st[r -- _length] .intval, st), ∀ j. j < 0 ∨ st[r -- _length] .intval ≤ j ⊦ r = jvmref, st[r -- _length] .intval = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(abstract_type)), 0 < i, is_integervalue(st[r -- _length]), r -- _length ∈ st, r -- _type ∈ st, r ∈ st, is_arrayref(r, i, st), ∀ j. j < 0 ∨ i ≤ j ⊦ r = jvmref, i = 0

Rule argument

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

Additional information

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