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Proof step 144 from proof validrefs-put-notin-03 (previous step)

is_valid_ref(str, r, st) ↔ is_valid_ref(str, r, st[r -- sk, val]), list2set(refs) ∩ list2set(refs0) = ∅ ⊦ val .refval = refs0 .first, refs0 .first = st[r -- sk] .refval, refs0 = [], sk = _type, sk = _length, validrefs(str, refs + r ' + refs0, ty, st[r -- sk, val]) ↔ validrefs(str, refs + r ' + refs0, ty, st), r ∈ refs0, r ∈ refs, dups(refs0), dups(refs)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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] → [refs0, r0, refs1] 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 : (refs0, r0, refs1)]]