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Proof step 13 from proof range-write-in (previous step)

key ∈ ri, ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1, ∃ key0. key0 ∈ ri[key, adr] ∧ ri[key, adr][key0] = adr0 ⊦ adr0 = adr, adr0 ≠ ri[key] ∧ (∃ key. key ∈ ri ∧ ri[key] = adr0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
key0 ∈ ri[key, adr], key ∈ ri, ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ ri[key, adr][key0] = adr, ri[key, adr][key0] ≠ ri[key] ∧ (∃ key1. key1 ∈ ri ∧ ri[key1] = ri[key, adr][key0])

Proof step 13 from proof range-write-in (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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