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Proof step 46 from proof cyclic-addrefarray (previous step)

newref(refs .first, st), type∃(str, ty), is_reftype(ty), dups(refs), validrefs(str, refs, mkarraytype(ty), addarray(refs .first, ty, vals, st)), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ ¬ cyclic(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ ty) ⊦ ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, refs .first = jvmref

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 45:
refs = r + refs0 ∧ refs ≠ [], newref(r, st), type∃(str, ty), is_reftype(ty), dups(refs), validrefs(str, refs, mkarraytype(ty), addarray(r, ty, vals, st)), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ ¬ cyclic(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ ty) ⊦ ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, r = jvmref

Rule argument

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

Additional information

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