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Proof step 11 from proof valid-indices-nodups-h (previous step)

n0 < # ar, φ(ar[n0]), ∀ ar0, φ0. ¬ dups(ar0.indicesWhere(φ0, n0)) ∨ ¬ n0 ≤ # ar0, dups(ar.indicesWhere(φ, n0)) ∨ n0 ∈ ar.indicesWhere(φ, n0) ∧ n = n0 ⊦

User applied rule case distinction

And obtained the following new goals

Proof step 12:
n0 < # ar, dups(ar.indicesWhere(φ, n0)), φ(ar[n0]), ∀ ar0, φ0. ¬ dups(ar0.indicesWhere(φ0, n0)) ∨ ¬ n0 ≤ # ar0 ⊦
Proof step 13:
n = n0, n0 < # ar, φ(ar[n0]), n0 ∈ ar.indicesWhere(φ, n0), ∀ ar0, φ0. ¬ dups(ar0.indicesWhere(φ0, n0)) ∨ ¬ n0 ≤ # ar0 ⊦

Rule argument

pos: left 4

Proof step 11 from proof valid-indices-nodups-h (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information