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Proof step 48 from proof junkrefs-put-notin-butlast (previous step)

acc + r ' = st[r0 -- i '] .refval ' + refs, 0 < st[r0 -- _length] .intval, 0 ≤ i, st[r0 -- _type] .type ≤ ty, r ∈ st, okval(val, ty0), okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), r -- mkfs(class, ty0, fieldvar) ' ∈ st, is_array(str, r0, st), junkrefs(str, acc + r ', st[r0 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', val]), is_referencevalue(st[r0 -- i ']), i < st[r0 -- _length] .intval, ∀ r, fs, st, val, str, ty. r -- fs ' ∈ st ∧ okval(st[r -- fs '], fs .type) ∧ okval(val, fs .type) ∧ r ∈ st → (junkrefs(str, acc + r ', ty, st[r -- fs ', val]) ↔ junkrefs(str, acc + r ', ty, st)) ∨ fs ' = _type ∨ fs ' = _length ∨ r ∈ acc ⊦ mkfs(class, ty0, fieldvar) ' = _length, mkfs(class, ty0, fieldvar) ' = _type, r0 = jvmref, r = r0, r ∈ acc, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ st[r0 -- i '] .refval = st[r0 -- i0 '] .refval ∧ junkrefs(str, st[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st), r ≠ st[r0 -- i '] .refval ∧ ¬ r ∈ refs, ¬ st[r0 -- i '] .refval ∈ acc ∧ st[r0 -- i '] .refval ≠ r

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 47:
st[r0 -- i '] = refval(r1), acc + r ' = r1 ' + refs, 0 < st[r0 -- _length] .intval, 0 ≤ i, st[r0 -- _type] .type ≤ ty, r ∈ st, okval(val, ty0), okval(st[r -- mkfs(class, ty0, fieldvar) '], ty0), r -- mkfs(class, ty0, fieldvar) ' ∈ st, is_array(str, r0, st), junkrefs(str, acc + r ', st[r0 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', val]), is_referencevalue(st[r0 -- i ']), i < st[r0 -- _length] .intval, ∀ r, fs, st, val, str, ty. r -- fs ' ∈ st ∧ okval(st[r -- fs '], fs .type) ∧ okval(val, fs .type) ∧ r ∈ st → (junkrefs(str, acc + r ', ty, st[r -- fs ', val]) ↔ junkrefs(str, acc + r ', ty, st)) ∨ fs ' = _type ∨ fs ' = _length ∨ r ∈ acc ⊦ mkfs(class, ty0, fieldvar) ' = _length, mkfs(class, ty0, fieldvar) ' = _type, r0 = jvmref, r = r0, r ∈ acc, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ r1 = st[r0 -- i0 '] .refval ∧ junkrefs(str, st[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st), r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r0 -- i '], r1] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r0 -- i '], r1)]]