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Proof step 7 from proof compatarray-abstract (previous step)

st[r -- _type] .type = mkarraytype(abstract_type), 0 < st[r -- _length] .intval, r ∈ st, is_integervalue(st[r -- _length]), r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → compat(str, st[r -- j '], abstract_type, st) ⊦ st[r -- _length] .intval = 0, r = jvmref

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
st[r -- _length] = intval(i), st[r -- _type] .type = mkarraytype(abstract_type), 0 < i, r ∈ st, is_integervalue(st[r -- _length]), r -- _length ∈ st, is_arrayref(r, i, st), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → compat(str, st[r -- j '], abstract_type, st) ⊦ i = 0, r = jvmref

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)]]