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Proof step 6 from proof compatarray-isarray-01 (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), okreftype(refval(r), mkarraytype(ty), st), is_integervalue(st[r -- _length]), is_arrayref(r, st[r -- _length] .intval, st), r ∈ st, r -- _length ∈ st, r -- _type ∈ st, j < st[r -- _length] .intval, 0 ≤ st[r -- _length] .intval, 0 ≤ j, 0 < st[r -- _length] .intval, ∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i → compat(str, st[r -- i '], ty, st), ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, compat(str, st[r -- j '], ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty)), okreftype(refval(r), mkarraytype(ty), st), is_integervalue(st[r -- _length]), is_arrayref(r, i0, st), r ∈ st, r -- _length ∈ st, r -- _type ∈ st, j < i0, 0 ≤ i0, 0 ≤ j, 0 < i0, ∀ i. ¬ i < 0 ∧ ¬ i0 ≤ i → compat(str, st[r -- i '], ty, st), ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, compat(str, st[r -- j '], ty, st)

Rule argument

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

Additional information

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