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Proof step 14 from proof valid-indices-nodups-h (previous step)

n0 < # ar, φ(ar[n0]), n0 ∈ ar.indicesWhere(φ, n0), ∀ ar0, φ0. ¬ dups(ar0.indicesWhere(φ0, n0)) ∨ ¬ n0 ≤ # ar0 ⊦

User applied rule apply lemma

And obtained the following new goals

Proof step 15:
⊦ n ≤ # ar ∧ m ∈ ar.indicesWhere(φ, n) → m < n

Rule argument

spec: <toplevel> name: valid-indices-indiceswhere-h-strong seq: ⊦ n ≤ # ar ∧ m ∈ ar.indicesWhere(φ, n) → m < n subst: [n, ar, m, φ] → [n0, ar, n0, φ]

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)% ⊦ ¬ n < n; (s) Used terms: n0, ar, n0, φ