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Proof step 8 from proof valid-indices-nodups-h (previous step)

n0 < # ar, dups(ar.indicesWhere(φ, n0) + n0 '), φ(ar[n0]), ∀ ar0, φ0. ¬ dups(ar0.indicesWhere(φ0, n0)) ∨ ¬ n0 ≤ # ar0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ dups(nx + nx0) ↔ dups(nx) ∨ dups(nx0) ∨ (∃ n. n ∈ nx ∧ n ∈ nx0)
Proof step 10:
n0 < # ar, φ(ar[n0]), ∀ ar0, φ0. ¬ dups(ar0.indicesWhere(φ0, n0)) ∨ ¬ n0 ≤ # ar0, dups(ar.indicesWhere(φ, n0)) ∨ dups(n0 ') ∨ (∃ n. n ∈ ar.indicesWhere(φ, n0) ∧ n ∈ n0 ') ⊦

Rule argument

spec: list-dup, inst: nat-list-set name: dups-appex seq: ⊦ dups(nx + nx0) ↔ dups(nx) ∨ dups(nx0) ∨ (∃ n. n ∈ nx ∧ n ∈ nx0) subst: [nx0, nx] → [n0 ', ar.indicesWhere(φ, n0)] flags: <all paths>

Additional information

Used terms: n0 ', ar.indicesWhere(φ, n0)