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Proof step 38 from proof isarray-update (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), r -- _type ∈ st, r ∈ st, r -- _length ∈ st, is_integervalue(st[r -- _length]), 0 ≤ st[r -- _length] .intval ⊦ r = jvmref, r = r0, is_arrayref(r, st[r -- _length] .intval, update(r0, fis, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → okval(st[r -- j '], ty)) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → okval(st[r -- j '], ty))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 37:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), r -- _type ∈ st, r ∈ st, r -- _length ∈ st, is_integervalue(st[r -- _length]), 0 ≤ i ⊦ r = jvmref, r = r0, is_arrayref(r, i, update(r0, fis, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty)) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ is_arrayref(r, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → okval(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)]]