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

m ∈ ar.indicesWhere(φ, n), n ≤ # ar, n ≤ m ⊦

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: n

Additional information

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