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Proof step 9 from proof cyclic-put-nopathex (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 8:
validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st[r0 -- sk, val]) ⊦ ¬ path∃(str, r, r0, st[r0 -- sk, val]), sk = _type, r0 = r, validrefs(str, (r ' + refs1) + r1 ', st[r -- _type] .type, st), path∃(str, r, r0, st), junkref(str, r, st), dups(refs1), r ∈ refs1, r1 ≠ r ∧ ¬ r1 ∈ refs1, r0 ≠ r1 ∧ ¬ r0 ∈ refs1

Rule argument

[CASEDARG : pos: right 10, ()]

Additional information

[[CONCRETESIMPRULES : ()]]