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Proof step 6 from proof cyclic-delete (previous step)

validrefs(str, r ' + refs0, st[r -- _type] .type, st -- r0) ⊦ r0 = r, ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

User applied rule exists right

And obtained the following new goals

Proof step 5:
⊦ ¬ validrefs(str, refs, ty, st) → ¬ validrefs(str, refs, ty, st -- r)

Rule argument

[EXRARG : pos: right 2, [extquanttermlist: (r ' + refs0) 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 : (r ' + refs0)]]