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Proof step 3 from proof valid-indices-nodups-h (previous step)

dups(ar.indicesWhere(φ, n)), n ≤ # ar ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 4:
⊦ ar.indicesWhere(φ, 0) = []
Proof step 5:
dups(ar.indicesWhere(φ, n0 +1)), n0 +1 ≤ # ar, ∀ ar, φ. ¬(dups(ar.indicesWhere(φ, n0)) ∧ n0 ≤ # ar) ⊦

Rule argument

indvar: n

Additional information

Used simplifier rules: indiceswhere-base: ⊦ ar.indicesWhere(φ, 0) = [];%nat freely generated by 0, +1;;% ⊦ 0 ≤ m; (s)% ⊦ ¬ dups([]); (s)