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Proof step 9 from proof okarray-01 (previous step)

j < st[r -- _length] .intval, okreftype(refval(r), mkarraytype(int_type), st), r -- _length ∈ st, is_integervalue(st[r -- _length]), is_arrayref(r, st[r -- _length] .intval, st), 0 ≤ j, 0 < st[r -- _length] .intval, r ∈ st, 0 ≤ st[r -- _length] .intval, ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → is_integervalue(st[r -- j ']) ⊦ r = r0, r = jvmref, is_integervalue(st[r -- j '])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
st[r -- _length] = intval(i), j < i, okreftype(refval(r), mkarraytype(int_type), st), r -- _length ∈ st, is_integervalue(st[r -- _length]), is_arrayref(r, i, st), 0 ≤ j, 0 < i, r ∈ st, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → is_integervalue(st[r -- j ']) ⊦ r = r0, r = jvmref, is_integervalue(st[r -- j '])

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)]]