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Proof step 55 from proof validrefs-junkrefs (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
⊦ validrefs(str, [], ty, st)
Proof step 54:
st[r -- i '] = refval(r0), junkrefs(str, r0 ' + refs1, 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) ∨ ¬ st[r0 -- _type] .type ≤ st[r -- _type] .type .type ⊦ r = jvmref, r0 = jvmref, validrefs(str, r ', ty, st) ∧ ( ¬ is_valid_ref(str, r0, st) ∨ is_obj(r, st) ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type) ∨ is_array(r, st) ∧ (∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval ∧ ¬ st[st[r -- i0 '] .refval -- _type] .type ≤ st[r -- _type] .type .type))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ' .last = r], [CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ ¬ r ∈ []], [CSIMPSEQ : ⊦ r ' + refs = r0 ' + refs0 ↔ r = r0 ∧ refs = refs0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ [] + refs = refs])]]