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Proof step 17 from proof validrefs-nodups (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ validrefs(str, refs + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, refs + r ' + refs1, ty, st)
Proof step 16:
validrefs(str, [] + r ' + refs0 + r ' + refs, ty, st) ∧ refs ≠ [] ∧ refs .last = jvmref → validrefs(str, [] + r ' + refs, ty, st), refs .last = jvmref, validrefs(str, r ' + refs0 + r ' + refs, ty, st), ∀ st, ty, str, refs1. # refs1 < # (r + (refs0 + (r + refs))) → ( validrefs(str, refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → (∃ refs3. validrefs(str, refs3, ty, st) ∧ refs3 ≠ [] ∧ refs3 .last = jvmref ∧ refs1 .first = refs3 .first ∧ ¬ dups(refs3) ∧ refs3 ⊆ refs1)) ⊦ refs = [], ∃ refs1. validrefs(str, refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref ∧ r = refs1 .first ∧ ¬ dups(refs1) ∧ refs1 ⊆ refs1 .first ' + refs0 + refs1 .first ' + refs

Rule argument

[LEMMAARG : validrefs-delcycle, [str, refs, r, refs0, refs1, ty, st] → [str, [], r, refs0, refs, ty, st]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, [], r, refs0, refs, ty, st)]]