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Proof step 38 from proof unchNorec-validrefs-pathex (previous step)

validrefs(str, refs, ty, st), r0 ∈ refs, ∀ r. r ∈ refs → unchangedNorec(r, st, st0) ⊦ refs = [], path∃(str, refs .first, r0, st0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 37:
refs = r1 + refs0, validrefs(str, refs, ty, st), r0 ∈ refs, ∀ r. r ∈ refs → unchangedNorec(r, st, st0) ⊦ refs = [], path∃(str, r1, r0, st0)

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: references lemma-name: elim-list-c antecedent: refs ≠ [] succedent: r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 substlist: [refs, r, refs0] → [refs, r1, refs0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs, r1, refs0)]]