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Proof step 13 from proof pathex-put-last (previous step)

validrefs(str, r ' + refs0, st[r -- _type] .type, st[(r ' + refs0) .last -- sk, val]) ⊦ sk = _type, r = (r ' + refs0) .last, path∃(str, r, (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 12:
r ' + refs0 = refs + r0 ' ∧ r ' + refs0 ≠ [], validrefs(str, r ' + refs0, st[r -- _type] .type, st[r0 -- sk, val]) ⊦ 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] → [r ' + refs0, r0, refs] ,T ,list-last ,references-olista ,last-elim ]

Additional information

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