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Proof step 27 from proof newrefs-new-01 (previous step)

∀ st. is_newref_list(newref_list(m, st), st), ∀ r. r ∈ newref_list(m, st[newref(st) -- 0 ', noval]) → r ≠ newref(st) ∧ r ≠ jvmref ∧ (∀ rk. rk ∈ st → rk .ref ≠ r) ⊦ is_newref_list(newref_list(m, st[newref(st) -- 0 ', noval]), st), dups(newref_list(m, st[newref(st) -- 0 ', noval]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ is_newref_list(refs, st) ↔ ¬ dups(refs) ∧ (∀ r. r ∈ refs → newref(r, st))
Proof step 26:
∀ st. is_newref_list(newref_list(m, st), st), ∀ r. r ∈ newref_list(m, st[newref(st) -- 0 ', noval]) → r ≠ newref(st) ∧ r ≠ jvmref ∧ (∀ rk. rk ∈ st → rk .ref ≠ r) ⊦ ¬ dups(newref_list(m, st[newref(st) -- 0 ', noval])) ∧ (∀ r. r ∈ newref_list(m, st[newref(st) -- 0 ', noval]) → newref(r, st)), dups(newref_list(m, st[newref(st) -- 0 ', noval]))

Rule argument

[crewrite-arg: list_ok , F , [st, refs] → [st, newref_list(m, st[newref(st) -- 0 ', noval])] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, newref_list(m, st[newref(st) -- 0 ', noval]))]]