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Proof step 9 from proof map-indices-append (previous step)

n < # ar, m < # ar, nx0 < # ar, ∀ ar, n, f. nx0 < # ar ∧ n < # ar → ar.mapIndices(nx0 + n ', f) = ar.mapIndices(nx0, f)[n, f(ar[n])] ∨ n ∈ nx0 ⊦ ar[m, f(ar[m])].mapIndices(nx0 + n ', f) = ar[m, f(ar[m])].mapIndices(nx0, f)[n, f(ar[n])], n = m, n ∈ nx0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 10:
nx0 < # ar, m < # ar, n < # ar, m < # ar[m, a], ∀ ar, n, f. nx0 < # ar ∧ n < # ar → ar.mapIndices(nx0 + n ', f) = ar.mapIndices(nx0, f)[n, f(ar[n])] ∨ n ∈ nx0 ⊦ ar[m, f(ar[m])].mapIndices(nx0 + n ', f) = ar[m, f(ar[m])].mapIndices(nx0, f)[n, f(ar[n])], n = m, n ∈ nx0

Rule argument

fma: m < # ar[m, a]

Additional information

Used simplifier rules: ⊦ # ar[n, a] = # ar; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used formulas: m < # ar[m, a]