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Proof step 10 from proof map-indices-append (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
n < # ar, nx0 < # ar, m < # 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

Rule argument

Additional information

Used simplifier rules: ⊦ # ar[n, a] = # ar; (s)