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Proof step 23 from proof junkref-put-nopathex-equiv-01 (previous step)

junkrefs(str, refs, st[refs .first -- _type] .type, st), is_valid_ref(str, r0, st) ⊦ sk = _type, refs = [], junkref(str, refs .first, st[r0 -- sk, val]), path∃(str, refs .first, r0, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
refs = r + refs0, junkrefs(str, refs, st[r -- _type] .type, st), is_valid_ref(str, r0, st) ⊦ sk = _type, refs = [], junkref(str, r, st[r0 -- sk, val]), path∃(str, r, r0, st)

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-list-c ]

Additional information

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