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Proof step 2 from proof index-update-range (previous step)

# kx = # ax, ax.toSet ∩ range ri = ∅, ri-inj(ri), kx.toSet ⊆ dom ri ⊦ range ri[kx, ax] = (range ri \ ri[kx].toSet) ∪ ax.toSet, dups(ax), dups(kx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information