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Proof step 25 from proof newrefs-new-01 (previous step)

r ∈ newref_list(m, st[newref(st) -- 0 ', noval]), ∀ 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])), newref(r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ r ∈ st → ¬ r ∈ newref_list(n, st)
Proof step 24:
¬ r ∈ st[newref(st) -- 0 ', noval], r ∈ newref_list(m, st[newref(st) -- 0 ', noval]), ∀ 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])), newref(r, st)

Rule argument

[crewrite-arg: newrefs-in , F , [st, n, r] → [st[newref(st) -- 0 ', noval], m, r] ]

Additional information

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