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Proof step 17 from proof range-write-in (previous step)

key ∈ ri, key0 ∈ ri, ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ ri[key0] = adr, key0 = key, ri[key0] ≠ ri[key] ∧ (∃ key1. key1 ∈ ri ∧ ri[key1] = ri[key0])

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 3

Additional information