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Proof step 1 from proof valid-indices-indiceswhere (conclusion)

⊦ valid-indices(ar, ar.indicesWhere(φ))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ valid-indices(ar, nx) ↔ (∀ n. n ∈ nx → n < # ar)
Proof step 3:
⊦ n ∈ ar.indicesWhere(φ) ↔ n < # ar ∧ φ(ar[n])

Rule argument

spec: <toplevel> name: valid-indices-nonrec seq: ⊦ valid-indices(ar, nx) ↔ (∀ n. n ∈ nx → n < # ar) subst: [nx, ar] → [ar.indicesWhere(φ), ar] flags: <all paths>

Additional information

Used simplifier rules: indices-where-in: ⊦ n ∈ ar.indicesWhere(φ) ↔ n < # ar ∧ φ(ar[n]); Used terms: ar.indicesWhere(φ), ar