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Proof step 37 from proof validrefs-nodups (previous step)

refs2 .last = jvmref, refs .last = jvmref, validrefs(str, (refs2 .first ' + refs1) + r0 ' + refs, ty, st), validrefs(str, refs2 .first ' + refs1 + r0 ' + refs0 + r0 ' + refs, ty, st), refs2 ⊆ (refs2 .first ' + refs1) + r0 ' + refs, validrefs(str, refs2, ty, st), ∀ st, ty, str, refs3. # refs3 < # (refs2 .first + (refs1 + (r0 + (refs0 + (r0 + refs))))) → ( validrefs(str, refs3, ty, st) ∧ refs3 ≠ [] ∧ refs3 .last = jvmref → (∃ refs1. validrefs(str, refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref ∧ refs3 .first = refs1 .first ∧ ¬ dups(refs1) ∧ refs1 ⊆ refs3)) ⊦ refs2 = [], refs2 .first = r0, refs = [], dups(refs2), refs2 .first ∈ refs1, refs2 .first ∈ refs0, refs2 .first ∈ refs, ∃ refs3. validrefs(str, refs3, ty, st) ∧ refs3 ≠ [] ∧ refs3 .last = jvmref ∧ refs2 .first = refs3 .first ∧ ¬ dups(refs3) ∧ refs3 ⊆ refs3 .first ' + refs1 + r0 ' + refs0 + r0 ' + refs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 36:
refs2 = r + refs4, refs2 .last = jvmref, refs .last = jvmref, validrefs(str, (r ' + refs1) + r0 ' + refs, ty, st), validrefs(str, r ' + refs1 + r0 ' + refs0 + r0 ' + refs, ty, st), refs2 ⊆ (r ' + refs1) + r0 ' + refs, validrefs(str, refs2, ty, st), ∀ st, ty, str, refs3. # refs3 < # (r + (refs1 + (r0 + (refs0 + (r0 + refs))))) → ( validrefs(str, refs3, ty, st) ∧ refs3 ≠ [] ∧ refs3 .last = jvmref → (∃ refs1. validrefs(str, refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref ∧ refs3 .first = refs1 .first ∧ ¬ dups(refs1) ∧ refs1 ⊆ refs3)) ⊦ refs2 = [], r = r0, refs = [], dups(refs2), r ∈ refs1, r ∈ refs0, r ∈ refs, ∃ refs3. validrefs(str, refs3, ty, st) ∧ refs3 ≠ [] ∧ refs3 .last = jvmref ∧ r = refs3 .first ∧ ¬ dups(refs3) ∧ refs3 ⊆ refs3 .first ' + refs1 + r0 ' + refs0 + r0 ' + refs

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs2, r, refs4] ,T ,list-data ,references ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs2, r, refs4)]]