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Proof step 14 from proof cyclic-put-statfield-01 (previous step)

validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ cyclic(str, r, st[jvmref -- sk, val]), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ cyclic(str, r, st) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st))
Proof step 13:
validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, (st[jvmref -- sk, val][r -- _type]) .type, st[jvmref -- sk, val]), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[jvmref -- sk, val], r, str)]]