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Proof step 9 from proof cyclic-addarray-other (previous step)

newref(r0, st), validrefs(str, r ' + refs0, st[r -- _type] .type, addarray(r0, ty, vals, st)), validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ r = r0, r0 = jvmref, r0 ∈ refs0, junkref(str, r, st), cyclic(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ cyclic(str, r, st) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st))
Proof step 8:
newref(r0, st), validrefs(str, r ' + refs0, st[r -- _type] .type, addarray(r0, ty, vals, st)), validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ r = r0, r0 = jvmref, r0 ∈ refs0, junkref(str, r, st), ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

[crewrite-arg: cyclic-def-simple, F, [st, r, str] → [st, r, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, str)]]