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Proof step 36 from proof junkrefs-put-notin-butlast (previous step)

acc + r ' = r1 ' + refs, 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_obj(str, r0, st), ∀ 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, junkrefs(str, (r0 ' + acc) + r ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ↔ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r1 = st[r0 -- fs '] .refval ∧ junkrefs(str, st[r0 -- fs '] .refval ' + refs, fs .type, st)), r ∈ acc, r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ junkrefs(str, refs, fs .type, st)))
Proof step 35:
is_obj(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∧ (st[r -- mkfs(class, ty0, fieldvar) ', val][r0 -- _type]) .type ≤ ty, acc + r ' = r1 ' + refs, 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_obj(str, r0, st), ∀ 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, acc + r ' ≠ [] ∧ (∃ fs. fs ' ∈ instfields((st[r -- mkfs(class, ty0, fieldvar) ', val][r0 -- _type]) .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ', val][r0 -- fs ']) ∧ (acc + r ') .first = (st[r -- mkfs(class, ty0, fieldvar) ', val][r0 -- fs ']) .refval ∧ junkrefs(str, acc + r ', fs .type, st[r -- mkfs(class, ty0, fieldvar) ', val])) ↔ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r1 = st[r0 -- fs '] .refval ∧ junkrefs(str, st[r0 -- fs '] .refval ' + refs, fs .type, st)), r ∈ acc, r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

Rule argument

[crewrite-arg: junkrefs-class , F , [st, ty, refs, r, str] → [st[r -- mkfs(class, ty0, fieldvar) ', val], ty, acc + r ', r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_obj (str, r0, st[r -- sk, val]) ↔ is_obj(str, r0, st))], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st[r -- mkfs(class, ty0, fieldvar) ', val], ty, acc + r ', r0, str)]]