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Proof step 4 from proof cyclic-not-null (previous step)

refs .first = jvmref, validrefs(str, refs, st[jvmref -- _type] .type, st), dups(refs) ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 2:
⊦ validrefs(str, [], ty, st)
Proof step 3:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []

Rule argument

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

Additional information

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