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Proof step 15 from proof pathex-put-last (previous step)

validrefs(str, refs, st[refs .first -- _type] .type, st[refs .last -- sk, val]) ⊦ sk = _type, refs = [], refs .first = refs .last, path∃(str, refs .first, refs .last, st), junkref(str, refs .first, st), dups(refs)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
refs = r + refs0, validrefs(str, refs, st[r -- _type] .type, st[refs .last -- sk, val]) ⊦ sk = _type, refs = [], r = refs .last, path∃(str, r, refs .last, st), junkref(str, r, st), dups(refs)

Rule argument

[speclemmaarg: ,refs ≠ [] → (r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0) ,[refs, r, refs0] → [refs, r, refs0] ,T ,list-data ,references-olista ,elim-1 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ refs ≠ [] → ( r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0)])], [EXTRATERMS : (refs, r, refs0)]]