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Proof step 7 from proof dups (previous step)

dups(set2list(s.butmin)), ∀ s0. # s0 < # s → dups(set2list(s0)) → false ⊦ # s = 0, s = ∅

User applied rule apply induction

And closed the goal!

Rule argument

subst: [s0] → [s.butmin]

Additional information

Used simplifier rules: ⊦ s ≠ ∅ → # s.butmin = # s - 1;% ⊦ m < 1 ↔ m = 0;% ⊦ ¬ m ≤ n ↔ n < m;%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ ¬ n < n;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: s.butmin