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Proof step 32 from proof cyclic-put-nopathex (previous step)

validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st) ⊦ sk = _type, path∃(str, r, r0, st), junkref(str, r, st), dups(refs1), r ∈ refs1, ∃ refs0, r1. ¬ dups(refs0) ∧ r1 ∈ refs0 ∧ refs0 .first = r ∧ validrefs(str, refs0 + r1 ', st[refs0 .first -- _type] .type, st[r0 -- sk, val]), r1 ≠ r ∧ ¬ r1 ∈ refs1

User applied rule exists right

And obtained the following new goals

Proof step 31:
validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st) ⊦ sk = _type, path∃(str, r, r0, st), junkref(str, r, st), dups(refs1), r ∈ refs1, ¬ dups(r ' + refs1) ∧ r1 ∈ r ' + refs1 ∧ (r ' + refs1) .first = r ∧ validrefs(str, (r ' + refs1) + r1 ', st[(r ' + refs1) .first -- _type] .type, st[r0 -- sk, val]), r1 ≠ r ∧ ¬ r1 ∈ refs1

Rule argument

[EXRARG : pos: right 6, [extquanttermlist: (r ' + refs1, r1) abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r ' + refs1, r1)]]