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Proof step 32 from proof cyclic-addarray-this-01 (previous step)

refs0 .first = vals[i→n(i)] .refval, 0 ≤ i, validrefs(str, refs0, ty, addarray(r0, ty, vals, st)), is_referencevalue(vals[i→n(i)]), i < n→i(# vals), newref(r0, st), is_array(str, r0, addarray(r0, ty, vals, st)), ∀ r. refval(r) ∈ vals → ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) ⊦ r0 = jvmref, refs0 = [], vals = [], ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 31:
refs0 = r1 + refs, r1 = vals[i→n(i)] .refval, 0 ≤ i, validrefs(str, refs0, ty, addarray(r0, ty, vals, st)), is_referencevalue(vals[i→n(i)]), i < n→i(# vals), newref(r0, st), is_array(str, r0, addarray(r0, ty, vals, st)), ∀ r. refval(r) ∈ vals → ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) ⊦ r0 = jvmref, refs0 = [], vals = [], ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs0, r1, refs] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

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