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Proof step 71 from proof exvalidrefs (previous step)

st[r0 -- _type] .type = st[r -- _type] .type, st[r -- mkfs(class, st[r -- _type] .type, fieldvar) '] = refval(r0), is_obj(str, r0, st), is_obj(str, r, st), mkfs(class, st[r -- _type] .type, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, r0 ' + refs0, st[r -- _type] .type, st), type∃(str, ty) → (ty ≤ st[r -- _type] .type → ty = st[r -- _type] .type), ∀ ty. type∃(str, ty) → (ty ≤ st[r -- _type] .type → ty = st[r -- _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, cyclic(str, r, st), r ∈ refs0, ∃ 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)), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref, ∃ refs. refs ≠ [] ∧ refs .first = r0 ∧ junkrefs(str, refs, st[refs .first -- _type] .type, st)

User applied rule exists right

And closed the goal!

Rule argument

[EXRARG : pos: right 8, [extquanttermlist: (r0 ' + refs0) abort:F , discard:T , computed:F ]]

Additional information

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