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Proof step 54 from proof validrefs-nodups (conclusion)

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

User applied rule induction

And obtained the following new goals

Proof step 53:
validrefs(str, refs, ty, st) ∧ refs ≠ [] ∧ refs .last = jvmref, ∀ 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)) ⊦ ∃ refs0. validrefs(str, refs0, ty, st) ∧ refs0 ≠ [] ∧ refs0 .last = jvmref ∧ refs .first = refs0 .first ∧ ¬ dups(refs0) ∧ refs0 ⊆ refs

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, # refs, [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (# refs)]]