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Proof step 30 from proof union-okarray (previous step)

st[r -- _type] .type = mkarraytype(ty0), r ∈ st, 0 ≤ st[r -- _length] .intval, ty0 ≤ ty, is_typevalue(st[r -- _type]), r -- _type ∈ st, is_arrayref(r, st[r -- _length] .intval, st), is_integervalue(st[r -- _length]), r -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st0 ∪ st) ∧ is_arrayref(r, st[r -- _length] .intval, st0 ∪ st) ∧ (0 ≤ j ∧ j < st[r -- _length] .intval → okval((st0 ∪ st)[r -- j '], ty))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
st[r -- _length] = intval(i), st[r -- _type] .type = mkarraytype(ty0), r ∈ st, 0 ≤ i, ty0 ≤ ty, is_typevalue(st[r -- _type]), r -- _type ∈ st, is_arrayref(r, i, st), is_integervalue(st[r -- _length]), r -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st0 ∪ st) ∧ is_arrayref(r, i, st0 ∪ st) ∧ (0 ≤ j ∧ j < i → okval((st0 ∪ st)[r -- j '], ty))

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)]]