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Proof step 19 from proof newrefs-last-01 (previous step)

newref_list(m, st[newref(st) -- 0 ', noval][newref(st[newref(st) -- 0 ', noval]) -- 0 ', noval]) .last = newref(st), ∀ st0. ¬ (newref(st0) ' + newref_list(m, st0[newref(st0) -- 0 ', noval])) .last ∈ newref_list(m, st0) ⊦ m = 0, newref(st) ∈ newref_list(m, st[newref(st) -- 0 ', noval])

User applied rule insert lemma

And obtained the following new goals

Proof step 16:
⊦ r ∈ newref_list(n, st) → newref(r, st)
Proof step 17:
⊦ newref_list(n, st) = [] ↔ n = 0
Proof step 18:
⊦ newref(r, st[r0 -- sk, val]) ↔ r ≠ r0 ∧ newref(r, st)

Rule argument

[LEMMAARG : newrefs-new, [r, n, st] → [newref_list (m, st[newref(st) -- 0 ', noval] [newref(st[newref(st) -- 0 ', noval]) -- 0 ', noval ]) .last, m, st[newref(st) -- 0 ', noval] [newref(st[newref(st) -- 0 ', noval]) -- 0 ', noval ]]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refs .last ∈ refs ↔ refs ≠ []])], [EXTRATERMS : (newref_list (m, st[newref(st) -- 0 ', noval] [newref(st[newref(st) -- 0 ', noval]) -- 0 ', noval ]) .last, m, st[newref(st) -- 0 ', noval] [newref(st[newref(st) -- 0 ', noval]) -- 0 ', noval ])]]