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Proof step 51 from proof validrefs-nodups (previous step)

refs .last = jvmref, validrefs(str, refs, ty, st), dups(refs), ∀ st, ty, str, refs0. # refs0 < # refs → ( validrefs(str, refs0, ty, st) ∧ refs0 ≠ [] ∧ refs0 .last = jvmref → (∃ refs1. validrefs(str, refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref ∧ refs0 .first = refs1 .first ∧ ¬ dups(refs1) ∧ refs1 ⊆ refs0)) ⊦ refs = [], ∃ refs0. validrefs(str, refs0, ty, st) ∧ refs0 ≠ [] ∧ refs0 .last = jvmref ∧ refs .first = refs0 .first ∧ ¬ dups(refs0) ∧ refs0 ⊆ refs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 50:
refs = r + refs2, refs .last = jvmref, validrefs(str, refs, ty, st), dups(refs), ∀ st, ty, str, refs0. # refs0 < # refs → ( validrefs(str, refs0, ty, st) ∧ refs0 ≠ [] ∧ refs0 .last = jvmref → (∃ refs1. validrefs(str, refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref ∧ refs0 .first = refs1 .first ∧ ¬ dups(refs1) ∧ refs1 ⊆ refs0)) ⊦ refs = [], ∃ refs0. validrefs(str, refs0, ty, st) ∧ refs0 ≠ [] ∧ refs0 .last = jvmref ∧ r = refs0 .first ∧ ¬ dups(refs0) ∧ refs0 ⊆ refs

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs, r, refs2] ,T ,list-data ,references ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs, r, refs2)]]