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Proof step 2 from proof valid-indices-indiceswhere-h (previous step)

n ≤ # ar ⊦ valid-indices(ar, ar.indicesWhere(φ, n))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ valid-indices(ar, nx) ↔ (∀ n. n ∈ nx → n < # ar)
Proof step 4:
n ≤ # ar ⊦ ∀ n0. n0 ∈ ar.indicesWhere(φ, n) → n0 < # ar

Rule argument

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

Additional information

Used terms: ar.indicesWhere(φ, n), ar