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Proof step 16 from proof index-update-in (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
# kx0 = # ax0, ∀ ax, key, ri. # ax0 = # ax → (key ∈ ri[kx0, ax] ↔ key ∈ ri ∨ key ∈ kx0) ⊦ key0 ∈ ri, key0 ∈ ri[key0, adr][kx0, ax0]

Proof step 16 from proof index-update-in (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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