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Proof step 10 from proof cyclic-addrefarray (previous step)

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

User applied rule exists right

And obtained the following new goals

Proof step 9:
⊦ ¬ validrefs(str, r ' + refs, st[r -- _type] .type, st) → ¬ validrefs(str, r ' + refs, ty, st)

Rule argument

[EXRARG : pos: right 10, [extquanttermlist: (r0 ' + 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 : (r0 ' + refs)]]