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Proof step 13 from proof map-ifn-at (previous step)

n < # ar, ar.indicesWhere(φ, m) < # ar, m ≤ # ar ⊦ (n ∈ ar.indicesWhere(φ, m) ⊃ f(ar[n]);ar[n]) = (n < m ∧ φ(ar[n]) ⊃ f(ar[n]);ar[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: indices-where-in-h seq: ⊦ m ≤ # ar → (n ∈ ar.indicesWhere(φ, m) ↔ n < m ∧ φ(ar[n])) subst: [m, φ, ar, n] → [m, φ, ar, n] flags: <all paths>

Additional information

Used terms: m, φ, ar, n