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Proof step 55 from proof exvalidrefs (previous step)

st[r -- _type] .type = st[r0 -- _type] .type, st[r -- mkfs(class, st[r0 -- _type] .type, fieldvar) '] = refval(r0), junkrefs(str, (r0 ' + refs) + r ', st[r0 -- _type] .type, st -- r), is_obj(str, r0, st), is_obj(str, r, st), mkfs(class, st[r0 -- _type] .type, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), type∃(str, ty) → (ty ≤ st[r0 -- _type] .type → ty = st[r0 -- _type] .type), ∀ ty. 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)) ⊦ r0 = jvmref, r = r0, r = jvmref, junkref(str, r0, st), r ∈ refs, validrefs(str, r0 ' + refs + r ', st[r0 -- _type] .type, st), ∃ fs. fs ' ∈ instfields(st[r0 -- _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)), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[crewrite-arg: validrefs-del-junkrefs , F , [st, ty, r, refs, r0, str] → [st, st[r0 -- _type] .type, r, refs, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ junkrefs(str, refs, ty0, st) ∧ ty ≤ ty0 → junkrefs(str, refs, ty, st)], [CSIMPSEQ : ⊦ ty ≤ ty])], [EXTRATERMS : (st, st[r0 -- _type] .type, r, refs, r0, str)]]