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Proof step 83 from proof validrefs-junkrefs (previous step)

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) ∧ 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) ∧ 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, ∃ refs, r0, refs0. r ' + r1 ' + refs1 = refs + r0 ' + refs0 ∧ validrefs(str, refs, ty, st) ∧ r0 ≠ jvmref ∧ ( ¬ is_valid_ref(str, r0, st) ∨ refs = [] ∧ ¬ st[r0 -- _type] .type ≤ ty ∨ refs ≠ [] ∧ ( 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) ∧ (∃ i. ¬ i < 0 ∧ ¬ st[refs .last -- _length] .intval ≤ i ∧ is_referencevalue(st[refs .last -- i ']) ∧ r0 = st[refs .last -- i '] .refval ∧ ¬ st[st[refs .last -- i '] .refval -- _type] .type ≤ st[refs .last -- _type] .type .type))), ¬ r1 ∈ refs ∧ r1 ≠ r0 ∧ ¬ r1 ∈ refs0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 82:
fs = mkfs(class, ty0, fieldvar), 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) ∧ 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 ≤ 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, ∃ refs, r0, refs0. r ' + r1 ' + refs1 = refs + r0 ' + refs0 ∧ validrefs(str, refs, ty, st) ∧ r0 ≠ jvmref ∧ ( ¬ is_valid_ref(str, r0, st) ∨ refs = [] ∧ ¬ st[r0 -- _type] .type ≤ ty ∨ refs ≠ [] ∧ ( 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) ∧ (∃ i. ¬ i < 0 ∧ ¬ st[refs .last -- _length] .intval ≤ i ∧ is_referencevalue(st[refs .last -- i ']) ∧ r0 = st[refs .last -- i '] .refval ∧ ¬ st[st[refs .last -- i '] .refval -- _type] .type ≤ st[refs .last -- _type] .type .type))), ¬ r1 ∈ refs ∧ r1 ≠ r0 ∧ ¬ r1 ∈ refs0

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [fs, class, ty0, fieldvar] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (fs, class, ty0, fieldvar)]]