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Proof step 9 from proof validrefs-nodups (previous step)

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

User applied rule exists right

And obtained the following new goals

Proof step 8:
refs .last = jvmref, refs4 .last = jvmref, validrefs(str, r ' + refs, ty, st), validrefs(str, r ' + refs0 + r ' + refs, ty, st), refs4 ⊆ r ' + refs, validrefs(str, r ' + refs4, ty, st), ∀ st, ty, str, refs2. # refs2 < # (r + (refs0 + (r + refs))) → ( validrefs(str, refs2, ty, st) ∧ refs2 ≠ [] ∧ refs2 .last = jvmref → (∃ refs3. validrefs(str, refs3, ty, st) ∧ refs3 ≠ [] ∧ refs3 .last = jvmref ∧ refs2 .first = refs3 .first ∧ ¬ dups(refs3) ∧ refs3 ⊆ refs2)) ⊦ refs4 = [], refs = [], dups(refs4), r ∈ refs4, validrefs(str, r ' + refs4, ty, st) ∧ r ' + refs4 ≠ [] ∧ (r ' + refs4) .last = jvmref ∧ r = (r ' + refs4) .first ∧ ¬ dups(r ' + refs4) ∧ r ' + refs4 ⊆ (r ' + refs4) .first ' + refs0 + (r ' + refs4) .first ' + refs

Rule argument

[EXRARG : pos: right 5, [extquanttermlist: (r ' + refs4) abort:F , discard:T , computed:T ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r ' + refs4)]]