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Proof step 1 from proof map-ifn-0 (conclusion)

⊦ ar.mapIf(φ, f, 0) = ar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n])
Proof step 3:
⊦ # ar.mapIf(φ, f, 0) = # ar ∧ (∀ n. n < # ar.mapIf(φ, f, 0) → ar.mapIf(φ, f, 0)[n] = ar[n])

Rule argument

spec: array name: Extension seq: ⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n]) subst: [ar2, ar1] → [ar, ar.mapIf(φ, f, 0)] flags: <all paths>

Additional information

Used terms: ar, ar.mapIf(φ, f, 0)