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Proof step 28 from proof junkref-update-equiv (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), is_obj(str, r, st), validFields(r0, fis, st), is_valid_ref(str, r0, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, r1 ' + acc, ty, st), ∀ r0, fis, st, str, r. validFields(r0, fis, st) ∧ is_valid_ref(str, r0, st) ∧ junkrefs(str, r ' + acc, st[r -- _type] .type, st) → junkref(str, r, update(r0, fis, st)) ∨ path∃(str, r, r0, st) ∨ _type ∈ fis ⊦ r = r0, r = jvmref, junkref(str, r, update(r0, fis, st)), path∃(str, r, r0, st), _type ∈ fis

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ is_obj(str, r, st) → ( junkref(str, r, st) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st))))
Proof step 27:
is_obj(str, r, update(r0, fis, st)), st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), is_obj(str, r, st), validFields(r0, fis, st), is_valid_ref(str, r0, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, r1 ' + acc, ty, st), ∀ r0, fis, st, str, r. validFields(r0, fis, st) ∧ is_valid_ref(str, r0, st) ∧ junkrefs(str, r ' + acc, st[r -- _type] .type, st) → junkref(str, r, update(r0, fis, st)) ∨ path∃(str, r, r0, st) ∨ _type ∈ fis ⊦ r = r0, r = jvmref, ∃ fs. fs ' ∈ instfields((update(r0, fis, st)[r -- _type]) .type .class) ∧ is_referencevalue(update(r0, fis, st)[r -- fs ']) ∧ (update(r0, fis, st)[r -- fs ']) .refval ≠ jvmref ∧ ( ¬ (update(r0, fis, st)[(update(r0, fis, st)[r -- fs ']) .refval -- _type]) .type ≤ fs .type ∨ junkref(str, (update(r0, fis, st)[r -- fs ']) .refval, update(r0, fis, st))), path∃(str, r, r0, st), _type ∈ fis

Rule argument

[speclemmaarg: , is_obj(str, r, st) → ( junkref(str, r, st) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ ( ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st)))) ,[st, r, str] → [update(r0, fis, st), r, str] ,F ,junkrefs , ,junkref-class ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_obj (str, r, update(r0, fis, st)) ↔ is_obj(str, r, st))])], [EXTRATERMS : (update(r0, fis, st), r, str)]]