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Proof step 30 from proof junkref-update-equiv (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), junkrefs(str, r1 ' + acc, ty, st), is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_valid_ref(str, r0, st), validFields(r0, fis, st), is_obj(str, r, 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 = jvmref, r = r0, _type ∈ fis, path∃(str, r, r0, st), junkref(str, r, update(r0, fis, st))

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- mkfs(class, ty, fieldvar) '], r1] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- mkfs(class, ty, fieldvar) '], r1)]]