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Proof step 70 from proof validrefs-junkrefs (previous step)

st[r -- i '] = refval(r2), validrefs(str, r2 ' + refs2, st[r -- _type] .type .type, st), junkrefs(str, r2 ' + refs2 + r0 ' + refs0, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, ¬ is_valid_ref(str, r0, st) ∨ is_obj((r2 ' + refs2) .last, st) ∧ mkfs(class, ty0, fieldvar) ' ∈ instfields(st[(r2 ' + refs2) .last -- _type] .type .class) ∧ is_referencevalue(st[(r2 ' + refs2) .last -- mkfs(class, ty0, fieldvar) ']) ∧ r0 = st[(r2 ' + refs2) .last -- mkfs(class, ty0, fieldvar) '] .refval ∧ ¬ st[st[(r2 ' + refs2) .last -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type ≤ ty0 ∨ is_array((r2 ' + refs2) .last, st) ∧ 0 ≤ i0 ∧ i0 < st[(r2 ' + refs2) .last -- _length] .intval ∧ is_referencevalue(st[(r2 ' + refs2) .last -- i0 ']) ∧ r0 = st[(r2 ' + refs2) .last -- i0 '] .refval ∧ ¬ st[st[(r2 ' + refs2) .last -- i0 '] .refval -- _type] .type ≤ st[(r2 ' + refs2) .last -- _type] .type .type ⊦ refs2 = [], r = jvmref, r0 = jvmref, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r -- i1 ']) ∧ r2 = st[r -- i1 '] .refval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 69:
st[r -- i '] = refval(r2), validrefs(str, r2 ' + refs2, st[r -- _type] .type .type, st), junkrefs(str, r2 ' + refs2 + r0 ' + refs0, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, ¬ is_valid_ref(str, r0, st) ∨ is_obj(refs2 .last, st) ∧ mkfs(class, ty0, fieldvar) ' ∈ instfields(st[refs2 .last -- _type] .type .class) ∧ is_referencevalue(st[refs2 .last -- mkfs(class, ty0, fieldvar) ']) ∧ r0 = st[refs2 .last -- mkfs(class, ty0, fieldvar) '] .refval ∧ ¬ st[st[refs2 .last -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type ≤ ty0 ∨ is_array(refs2 .last, st) ∧ 0 ≤ i0 ∧ i0 < st[refs2 .last -- _length] .intval ∧ is_referencevalue(st[refs2 .last -- i0 ']) ∧ r0 = st[refs2 .last -- i0 '] .refval ∧ ¬ st[st[refs2 .last -- i0 '] .refval -- _type] .type ≤ st[refs2 .last -- _type] .type .type ⊦ refs2 = [], r = jvmref, r0 = jvmref, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r -- i1 ']) ∧ r2 = st[r -- i1 '] .refval

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs ≠ [] → (r ' + refs) .last = refs .last])]]