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Proof step 8 from proof cyclic-addarray-this (previous step)

refs0 .first = jvmref, newref(r, st), is_valid_ref(str, r, addarray(r, ty, i, st)), type∃(str, ty), 0 ≤ i, i0 < i, is_referencevalue(initial_value(ty)), validrefs(str, refs0, ty, addarray(r, ty, i, st)), 0 ≤ i0, 0 < i ⊦ refs0 = [], r = jvmref, ty .jtelemtype = void_type, ty .jtelemtype = abstract_type, ¬ r ∈ refs0 ∧ ¬ dups(refs0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs0, r0, refs] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r + refs = r ' + refs], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ ¬ ¬ (r ∈ refs ∨ dups(refs))], [CSIMPSEQ : ⊦ ¬ r ∈ []], [CSIMPSEQ : ⊦ ¬ dups([])], [CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs0, r0, refs)]]