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Proof step 9 from proof validrefs-applast-array-null (previous step)

st[r -- _type] = typeval(mkarraytype(ty0)), type∃(str, ty0), validrefs(str, refs + r ', ty, st), r ∈ st, 0 < st[r -- _length] .intval, 0 ≤ i, is_reftype(ty0), i < st[r -- _length] .intval, r -- _type ∈ st, okreftype(refval(r), mkarraytype(ty0), st), r -- _length ∈ st, is_integervalue(st[r -- _length]), is_arrayref(r, st[r -- _length] .intval, st), 0 ≤ st[r -- _length] .intval, ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → is_referencevalue(st[r -- j ']) ⊦ ty0 .jtelemtype = void_type, ty0 .jtelemtype = abstract_type, r = jvmref, is_referencevalue(st[r -- i ']), validrefs(str, refs + r ' + jvmref ', ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty0)), type∃(str, ty0), validrefs(str, refs + r ', ty, st), r ∈ st, 0 < i0, 0 ≤ i, is_reftype(ty0), i < i0, r -- _type ∈ st, okreftype(refval(r), mkarraytype(ty0), st), r -- _length ∈ st, is_integervalue(st[r -- _length]), is_arrayref(r, i0, st), 0 ≤ i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_referencevalue(st[r -- j ']) ⊦ ty0 .jtelemtype = void_type, ty0 .jtelemtype = abstract_type, r = jvmref, is_referencevalue(st[r -- i ']), validrefs(str, refs + r ' + jvmref ', 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)]]