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Proof step 4 from proof dups (previous step)

dups(set2list(s)), ∀ s0. # s0 < # s → dups(set2list(s0)) → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ s ≠ ∅ → set2list(s) = s.min + set2list(s.butmin)
Proof step 6:
s ≠ ∅, dups(s.min + set2list(s.butmin)), ∀ s0. # s0 < # s → dups(set2list(s0)) → false ⊦

Rule argument

name: set2list-rec rotate: F subst: [s] → [s]

Additional information

Used simplifier rules: set2list-empty: ⊦ set2list(∅) = [];% ⊦ ¬ dups([]); Used terms: s