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Proof step 2 from proof ri-inj-write (previous step)

ri-inj(ri) ⊦ ri-inj(ri[key, adr]), adr ∈ ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
ri[key, adr][key0] = ri[key, adr][key1], key0 ∈ ri[key, adr], key1 ∈ ri[key, adr], ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ key0 = key1, adr ∈ ri

Rule argument

Additional information

Used simplifier rules: ri-inj: ⊦ ri-inj(ri) ↔ (∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1);