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Proof step 12 from proof cyclic-class (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), st[r0 -- _type] .type ≤ ty, is_reftype(ty), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), validrefs(str, r0 ' + refs0, st[r0 -- _type] .type, st) ⊦ ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st), ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

User applied rule exists right

And obtained the following new goals

Proof step 11:
st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), st[r0 -- _type] .type ≤ ty, is_reftype(ty), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), validrefs(str, r0 ' + refs0, st[r0 -- _type] .type, st) ⊦ dups(r ' + r0 ' + refs0) ∧ (r ' + r0 ' + refs0) .first = r ∧ validrefs(str, r ' + r0 ' + refs0, st[(r ' + r0 ' + refs0) .first -- _type] .type, st), ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

[EXRARG : pos: right 1, [extquanttermlist: (r ' + r0 ' + refs0) abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r ' + r0 ' + refs0)]]