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Proof step 1 from proof ri-inj-variant1-01 (conclusion)

⊦ ri-inj(ri) → ( ri-inj(ri0) ↔ (∀ key0, key1. (key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1) → key0 ∈ ri0 ∧ key1 ∈ ri0 ∧ ri0[key0] = ri0[key1] → key0 = key1))

System applied rule normalize

And obtained the following new goals

Proof step 2:
ri-inj(ri) ⊦ ri-inj(ri0) ↔ (∀ key0, key1. (key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1) → key0 ∈ ri0 ∧ key1 ∈ ri0 ∧ ri0[key0] = ri0[key1] → key0 = key1)

Proof step 1 from proof ri-inj-variant1-01 (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information