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Proof step 10 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 ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty0, st)) ⊦ r = jvmref, ty0 .jtelemtype = void_type, ty0 .jtelemtype = abstract_type, 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 9:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ is_reftype(ty) → ( okval(val, ty) ↔ is_referencevalue(val))], [CSIMPSEQ : ⊦ oktype(val, ty, st) ↔ okval(val, ty)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]