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Proof step 23 from proof cyclic-def-simple (previous step)

validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st) ⊦ is_obj(str, r, st), ∃ refs0. dups(refs0) ∧ refs0 .first = r ∧ validrefs(str, refs0, st[refs0 .first -- _type] .type, st), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ r = jvmref → (validrefs(str, r ' + refs, ty, st) ↔ refs = [])
Proof step 22:
r ≠ jvmref, validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st) ⊦ is_obj(str, r, st), ∃ refs0. dups(refs0) ∧ refs0 .first = r ∧ validrefs(str, refs0, st[refs0 .first -- _type] .type, st), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

Rule argument

[crewrite-arg: validrefs-null , F , [st, ty, refs, r, str] → [st, mkclasstype(`java.lang.Object' .class), refs1, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_obj(str, jvmref, st)], [CSIMPSEQ : ⊦ ¬ r ∈ []], [CSIMPSEQ : ⊦ ¬ dups([])])], [EXTRATERMS : (st, mkclasstype(`java.lang.Object' .class), refs1, r, str)]]