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Proof step 5 from proof valid-indices-indiceswhere-h (previous step)

n0 ∈ ar.indicesWhere(φ, n), n ≤ # ar, # ar ≤ n0, n ≤ n0 ⊦

User applied rule apply lemma

And obtained the following new goals

Proof step 6:
⊦ 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] → [n, ar, n0, φ]

Additional information

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