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Proof step 8 from proof validrefs-junkrefs (previous step)

st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), junkrefs(str, r0 ' + refs1, ty1, st), st[r -- _type] .type ≤ ty, is_obj(str, r, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ¬ is_valid_ref(str, r0, st) ∨ ¬ st[r0 -- _type] .type ≤ ty1, ∀ str0, ty0, st0. junkrefs(str0, r0 ' + refs1, ty0, st0) → (∃ refs, r, refs0. r0 ' + refs1 = refs + r ' + refs0 ∧ validrefs(str0, refs, ty0, st0) ∧ r ≠ jvmref ∧ ( ¬ is_valid_ref(str0, r, st0) ∨ refs = [] ∧ ¬ st0[r -- _type] .type ≤ ty0 ∨ refs ≠ [] ∧ ( is_obj(refs .last, st0) ∧ (∃ fs. fs ' ∈ instfields(st0[refs .last -- _type] .type .class) ∧ is_referencevalue(st0[refs .last -- fs ']) ∧ r = st0[refs .last -- fs '] .refval ∧ ¬ st0[st0[refs .last -- fs '] .refval -- _type] .type ≤ fs .type) ∨ is_array(refs .last, st0) ∧ (∃ i. 0 ≤ i ∧ i < st0[refs .last -- _length] .intval ∧ is_referencevalue(st0[refs .last -- i ']) ∧ r = st0[refs .last -- i '] .refval ∧ ¬ st0[st0[refs .last -- i '] .refval -- _type] .type ≤ st0[refs .last -- _type] .type .type)))) ⊦ r = jvmref, r0 = jvmref, (r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty) ∧ ( ¬ 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) ∧ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ ¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), junkrefs(str, r0 ' + refs1, ty1, st), st[r -- _type] .type ≤ ty, is_obj(str, r, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_valid_ref(str, r0, st), is_obj(r, st), ∀ str0, ty0, st0. junkrefs(str0, r0 ' + refs1, ty0, st0) → (∃ refs, r, refs0. r0 ' + refs1 = refs + r ' + refs0 ∧ validrefs(str0, refs, ty0, st0) ∧ r ≠ jvmref ∧ ( ¬ is_valid_ref(str0, r, st0) ∨ refs = [] ∧ ¬ st0[r -- _type] .type ≤ ty0 ∨ refs ≠ [] ∧ ( is_obj(refs .last, st0) ∧ (∃ fs. fs ' ∈ instfields(st0[refs .last -- _type] .type .class) ∧ is_referencevalue(st0[refs .last -- fs ']) ∧ r = st0[refs .last -- fs '] .refval ∧ ¬ st0[st0[refs .last -- fs '] .refval -- _type] .type ≤ fs .type) ∨ is_array(refs .last, st0) ∧ (∃ i. 0 ≤ i ∧ i < st0[refs .last -- _length] .intval ∧ is_referencevalue(st0[refs .last -- i ']) ∧ r = st0[refs .last -- i '] .refval ∧ ¬ st0[st0[refs .last -- i '] .refval -- _type] .type ≤ st0[refs .last -- _type] .type .type)))) ⊦ r = jvmref, r0 = jvmref, st[r0 -- _type] .type ≤ ty1, ∃ 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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_obj(r, st) → ¬ is_array(r, st)], [CSIMPSEQ : ⊦ ¬ is_obj(r, st) → ¬ is_obj(str, r, st)], [CSIMPSEQ : ⊦ is_obj(str, r, st) → is_valid_ref(str, r, st)])]]