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Proof step 11 from proof map-indices-at (previous step)

nx0 < # ar, m < # ar, m < # ar[m, a], ∀ ar0, n0, f0. nx0 < # ar0 ∧ n0 < # ar0 → ar0.mapIndices(nx0, f0)[n0] = (n0 ∈ nx0 ⊃ f0(ar0[n0]);ar0[n0]) ⊦ ar[m, f(ar[m])].mapIndices(nx0, f)[m] = f(ar[m]), dups(nx0), m ∈ nx0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
nx0 < # ar, m < # ar, ∀ ar0, n0, f0. nx0 < # ar0 ∧ n0 < # ar0 → ar0.mapIndices(nx0, f0)[n0] = (n0 ∈ nx0 ⊃ f0(ar0[n0]);ar0[n0]) ⊦ ar[m, f(ar[m])].mapIndices(nx0, f)[m] = f(ar[m]), dups(nx0), m ∈ nx0

Rule argument

Additional information

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