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Proof step 52 from proof cyclic-def-simple (previous step)

⊦ cyclic(str, r, st) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)), is_obj(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ cyclic(str, r, st) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st))
Proof step 51:
⊦ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st)) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)), is_obj(str, r, st)

Rule argument

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

Additional information

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