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Proof step 9 from proof cyclic-subset-01 (previous step)

st ⊆ st0, validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ junkref(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0), (dups(refs0) ∨ r ∈ refs0) ∧ validrefs(str, r ' + refs0, st0[r -- _type] .type, st0)

User applied rule case distinction

And obtained the following new goals

Proof step 8:
st ⊆ st0, validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ validrefs(str, r ' + refs0, st0[r -- _type] .type, st0), junkref(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

[CASEDARG : pos: right 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]