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Proof step 88 from proof validrefs-lastelem (previous step)

st[r0 -- i '] = refval(jvmref), st[r0 -- _type] = typeval(mkarraytype(ty0)), r0 -- _type ∈ st, okreftype(refval(r0), mkarraytype(ty0), st), r0 -- _length ∈ st, is_arrayref(r0, st[r0 -- _length] .intval, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, is_array(str, r0, st), mkarraytype(ty0) ≤ ty, i < st[r0 -- _length] .intval, r0 ∈ st, 0 ≤ st[r0 -- _length] .intval, ∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → okval(st[r0 -- j '], ty0) ⊦ ty0 = void_type, r0 = jvmref, is_reftype(ty0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 87:
st[r0 -- _length] = intval(i0) ∧ is_integervalue(st[r0 -- _length]), st[r0 -- i '] = refval(jvmref), st[r0 -- _type] = typeval(mkarraytype(ty0)), r0 -- _type ∈ st, okreftype(refval(r0), mkarraytype(ty0), st), r0 -- _length ∈ st, is_arrayref(r0, i0, st), 0 ≤ i, 0 < i0, is_array(str, r0, st), mkarraytype(ty0) ≤ ty, i < i0, r0 ∈ st, 0 ≤ i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r0 -- j '], ty0) ⊦ ty0 = void_type, r0 = jvmref, is_reftype(ty0)

Rule argument

[speclemmaarg: ,is_integervalue(val) → (i = val .intval ↔ val = intval(i)) ,[val, i] → [st[r0 -- _length], i0] ,T ,javavalue , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_integervalue(val) → val .intval = 0], [CSIMPELIM : ⊦ is_integervalue(val) → ( i = val .intval ↔ val = intval(i))])], [EXTRATERMS : (st[r0 -- _length], i0)]]