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Proof step 65 from proof validrefs-junkrefs (previous step)

validrefs(str, r ' + refs, ty, st), r1 ' + refs1 = refs + r0 ' + refs0, st[r -- i '] = refval(r1), validrefs(str, refs, st[r -- _type] .type .type, st), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), r1 ∈ refs, ¬ is_valid_ref(str, r0, st) ∨ is_obj(refs .last, st) ∧ mkfs(class, ty0, fieldvar) ' ∈ instfields(st[refs .last -- _type] .type .class) ∧ is_referencevalue(st[refs .last -- mkfs(class, ty0, fieldvar) ']) ∧ r0 = st[refs .last -- mkfs(class, ty0, fieldvar) '] .refval ∧ ¬ st[st[refs .last -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type ≤ ty0 ∨ is_array(refs .last, st) ∧ 0 ≤ i0 ∧ i0 < st[refs .last -- _length] .intval ∧ is_referencevalue(st[refs .last -- i0 ']) ∧ r0 = st[refs .last -- i0 '] .refval ∧ ¬ st[st[refs .last -- i0 '] .refval -- _type] .type ≤ st[refs .last -- _type] .type .type ⊦ refs = [], r0 = jvmref, r = jvmref, validrefs(str, r ' + refs, ty, st) ∧ ( ¬ is_valid_ref(str, r0, st) ∨ is_obj(refs .last, st) ∧ (∃ fs. fs ' ∈ instfields(st[refs .last -- _type] .type .class) ∧ is_referencevalue(st[refs .last -- fs ']) ∧ r0 = st[refs .last -- fs '] .refval ∧ ¬ st[st[refs .last -- fs '] .refval -- _type] .type ≤ fs .type) ∨ is_array(refs .last, st) ∧ (∃ i1. ¬ i1 < 0 ∧ ¬ st[refs .last -- _length] .intval ≤ i1 ∧ is_referencevalue(st[refs .last -- i1 ']) ∧ r0 = st[refs .last -- i1 '] .refval ∧ ¬ st[st[refs .last -- i1 '] .refval -- _type] .type ≤ st[refs .last -- _type] .type .type))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
r1 ' + refs1 = refs + r0 ' + refs0, st[r -- i '] = refval(r1), validrefs(str, r ' + refs, ty, st), validrefs(str, refs, st[r -- _type] .type .type, st), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), r1 ∈ refs, is_valid_ref(str, r0, st), is_obj(refs .last, st) ∧ mkfs(class, ty0, fieldvar) ' ∈ instfields(st[refs .last -- _type] .type .class) ∧ is_referencevalue(st[refs .last -- mkfs(class, ty0, fieldvar) ']) ∧ r0 = st[refs .last -- mkfs(class, ty0, fieldvar) '] .refval ∧ ¬ st[st[refs .last -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type ≤ ty0 ∨ is_array(refs .last, st) ∧ 0 ≤ i0 ∧ i0 < st[refs .last -- _length] .intval ∧ is_referencevalue(st[refs .last -- i0 ']) ∧ r0 = st[refs .last -- i0 '] .refval ∧ ¬ st[st[refs .last -- i0 '] .refval -- _type] .type ≤ st[refs .last -- _type] .type .type ⊦ refs = [], r0 = jvmref, r = jvmref, is_obj(refs .last, st) ∧ (∃ fs. fs ' ∈ instfields(st[refs .last -- _type] .type .class) ∧ is_referencevalue(st[refs .last -- fs ']) ∧ r0 = st[refs .last -- fs '] .refval ∧ ¬ st[st[refs .last -- fs '] .refval -- _type] .type ≤ fs .type), is_array(refs .last, st) ∧ (∃ i1. ¬ i1 < 0 ∧ ¬ st[refs .last -- _length] .intval ≤ i1 ∧ is_referencevalue(st[refs .last -- i1 ']) ∧ r0 = st[refs .last -- i1 '] .refval ∧ ¬ st[st[refs .last -- i1 '] .refval -- _type] .type ≤ st[refs .last -- _type] .type .type)

Rule argument

[emptyarg]

Additional information

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