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Proof step 7 from proof valid-indices-nodups-h (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 8:
n0 < # ar, dups(ar.indicesWhere(φ, n0) + n0 '), φ(ar[n0]), ∀ ar0, φ0. ¬ dups(ar0.indicesWhere(φ0, n0)) ∨ ¬ n0 ≤ # ar0 ⊦
Proof step 16:
n0 < # ar, dups(ar.indicesWhere(φ, n0) + []), ∀ ar0, φ0. ¬ dups(ar0.indicesWhere(φ0, n0)) ∨ ¬ n0 ≤ # ar0 ⊦ φ(ar[n0])

Rule argument

pos: left 2

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