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Proof step 27 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] = ri[key], key0 ∈ ri[key, adr] ∧ ri[key, adr][key0] = ri[key0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
key ∈ ri, key0 ∈ ri, key0 ∈ ri[key, adr], ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ ri[key0] = ri[key], ri[key, adr][key0] = ri[key0]

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)