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Proof step 11 from proof pathex-put-last (previous step)

r ' + refs0 = refs + refs0 .last ', r ∈ refs, validrefs(str, r ' + refs0, st[r -- _type] .type, st[refs0 .last -- sk, val]) ⊦ refs0 = [], sk = _type, r = refs0 .last, path∃(str, r, refs0 .last, st), junkref(str, r, st), dups(refs0), r ∈ refs0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
refs0 = refs1 + r0 ', r ' + refs0 = refs + r0 ', r ∈ refs, validrefs(str, r ' + refs0, st[r -- _type] .type, st[r0 -- sk, val]) ⊦ refs0 = [], sk = _type, r = r0, path∃(str, r, r0, st), junkref(str, r, st), dups(refs0), r ∈ refs0

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r ' ,[refs, r, refs0] → [refs0, r0, refs1] ,T ,list-last ,references-olista ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r '])], [EXTRATERMS : (refs0, r0, refs1)]]