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Proof step 83 from proof exvalidrefs (previous step)

st[r -- mkfs(class, st[r -- _type] .type, fieldvar) '] = refval(r0), mkfs(class, st[r -- _type] .type, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), st[r0 -- _type] .type ≤ st[r -- _type] .type, is_obj(str, r0, st), junkref(str, r0, st -- r), ∀ ty. type∃(str, ty) → (ty ≤ st[r -- _type] .type → ty = st[r -- _type] .type), type∃(str, ty) → (ty ≤ st[r0 -- _type] .type → ty = st[r0 -- _type] .type), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∀ ty. type∃(str, ty) → (ty ≤ st0[r -- _type] .type ↔ ty = st0[r -- _type] .type)) ∧ (∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ fs .type = st0[r -- _type] .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = jvmref, r = r0, r0 = jvmref, cyclic(str, r, st), junkref(str, r0, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st[r -- fs ']) ∨ ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , junkref(str, r, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ junkrefs(str, refs, st[r -- _type] .type, st)) ,[st, r, str] → [st -- r, r0, str] ,F ,junkrefs , ,junkref-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st -- r, r0, str)]]