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Proof step 8 from proof ri-inj-variant1-01 (previous step)

ri0[key0] = ri0[key], key ∈ ri0, key0 ∈ ri0, ¬ key0 ∈ ri ∨ ¬ key ∈ ri ∨ ri[key0] ≠ ri[key] → key0 ∈ ri0 ∧ key ∈ ri0 ∧ ri0[key0] = ri0[key] → key0 = key, ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ key0 = key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
ri0[key0] = ri0[key], ri[key0] = ri[key], key0 ∈ ri0, key ∈ ri0, key0 ∈ ri, key ∈ ri, ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ key0 = key

Proof step 8 from proof ri-inj-variant1-01 (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information