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Proof step 12 from proof unchanged-pathex (previous step)

validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st), unchanged(str, refs .first, st, st1) ⊦ refs = [], validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
refs = r + refs0, validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st), unchanged(str, r, st, st1) ⊦ refs = [], validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st1)

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, r, 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, r, refs0)]]