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Proof step 9 from proof update-index-shift (previous step)

# ax0 = # kx0, ∀ ax, ri, key, adr. # ax = # kx0 → ri[key, adr][kx0, ax] = ri[kx0, ax][key, adr] ∨ key ∈ kx0 ⊦ ri[key0, adr0][key, adr][kx0, ax0] = ri[key0, adr0][kx0, ax0][key, adr], key0 = key, key ∈ kx0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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