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Proof step 1 from proof index-update-range (conclusion)

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

System applied rule normalize

And obtained the following new goals

Proof step 2:
# 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)

Proof step 1 from proof index-update-range (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information