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Proof step 16 from proof indices-where-in-h (previous step)

m0 < # ar, n < # ar, φ(ar[n]), n ≤ m0, ∀ ar, n, φ. m0 ≤ # ar → (n ∈ ar.indicesWhere(φ, m0) ↔ n < m0 ∧ φ(ar[n])) ⊦ φ(ar[m0]), n ∈ ar.indicesWhere(φ, m0)

Heuristic quantifier applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: ar, n, φ

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s) Used terms: ar, n, φ