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Proof step 10 from proof cyclic-addarray-this-01 (previous step)

vals[i→n(i)] = refval(r1), refval(r1) ∈ vals, validrefs(str, r1 ' + refs, ty, addarray(r0, ty, vals, st)), 0 ≤ i, is_array(str, r0, addarray(r0, ty, vals, st)), newref(r0, st), i < n→i(# vals), validrefs(str, r1 ' + refs, ty, st), ∀ r. refval(r) ∈ vals → ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) ⊦ vals = [], r0 = jvmref, r0 = r1, r0 ∈ refs, junkref(str, r1, st), ¬ dups(refs) ∧ ¬ r1 ∈ refs, ∃ refs0. dups(refs0) ∧ refs0 .first = r1 ∧ validrefs(str, refs0, st[refs0 .first -- _type] .type, st)

User applied rule exists right

And obtained the following new goals

Rule argument

[EXRARG : pos: right 7, [extquanttermlist: (r1 ' + refs) abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r])], [EXTRATERMS : (r1 ' + refs)]]