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

n0 < m, n0 < # ar, ∀ m0, ar0, φ0. ¬ m0 ∈ ar0.indicesWhere(φ0, n0) ∨ ¬ n0 ≤ # ar0 ∨ ¬ n0 ≤ m0, m ∈ ar.indicesWhere(φ, n0) ∨ m ∈ (φ(ar[n0]) ⊃ n0 ';[]) ⊦

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 8:
n0 < # ar, n0 < m, m ∈ ar.indicesWhere(φ, n0), ∀ m0, ar0, φ0. ¬ m0 ∈ ar0.indicesWhere(φ0, n0) ∨ ¬ n0 ≤ # ar0 ∨ ¬ n0 ≤ m0 ⊦
Proof step 9:
n0 < # ar, n0 < m, m ∈ (φ(ar[n0]) ⊃ n0 ';[]), ∀ m0, ar0, φ0. ¬ m0 ∈ ar0.indicesWhere(φ0, n0) ∨ ¬ n0 ≤ # ar0 ∨ ¬ n0 ≤ m0 ⊦

Rule argument

pos: left 4

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

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Rule argument

Additional information