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Proof step 13 from proof newrefs-butlast-01 (previous step)

∀ st. newref_list(m + 1, st) .butlast = newref_list(m, st) ⊦ (newref(st) ' + newref_list(1 + m, st[newref(st) -- 0 ', noval])) .butlast = newref(st) ' + newref_list(m, st[newref(st) -- 0 ', noval])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ refs ≠ [] → (r ' + refs) .butlast = r ' + refs .butlast
Proof step 10:
¬ newref_list(1 + m, st[newref(st) -- 0 ', noval]) ≠ [], ∀ st. newref_list(m + 1, st) .butlast = newref_list(m, st) ⊦ (newref(st) ' + newref_list(1 + m, st[newref(st) -- 0 ', noval])) .butlast = newref(st) ' + newref_list(m, st[newref(st) -- 0 ', noval])
Proof step 12:
newref_list(1 + m, st[newref(st) -- 0 ', noval]) ≠ [], ∀ st. newref_list(m + 1, st) .butlast = newref_list(m, st) ⊦ newref(st) ' + newref_list(1 + m, st[newref(st) -- 0 ', noval]) .butlast = newref(st) ' + newref_list(m, st[newref(st) -- 0 ', noval])

Rule argument

[speclemmaarg: ,refs ≠ [] → (r ' + refs) .butlast = r ' + refs .butlast ,[refs, r] → [newref_list(1 + m, st[newref(st) -- 0 ', noval]), newref(st)] ,F ,list-last ,references ,bc ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (newref_list(1 + m, st[newref(st) -- 0 ', noval]), newref(st))]]