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Proof step 8 from proof validrefs-applast-array-null (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
st[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = intval(i0), 0 ≤ i0, 0 < i0, is_arrayref(r, i0, st), r -- _length ∈ st, okreftype(refval(r), mkarraytype(ty0), st), r -- _type ∈ st, i < i0, is_reftype(ty0), 0 ≤ i, r ∈ st, validrefs(str, refs + r ', ty, st), type∃(str, ty0), ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_referencevalue(st[r -- j ']) ⊦ r = jvmref, ty0 .jtelemtype = abstract_type, ty0 .jtelemtype = void_type, validrefs(str, refs + r ' + jvmref ', ty, st), is_referencevalue(st[r -- i '])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_integervalue(intval(i))], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j])]]