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Proof step 5 from proof replay-nonorphans-trunc (previous step)

⊦ key ∈ ro, ∀ key0. (key0 ∈ (ri ⊖ ro) \ datakeys(key, n, ri) ↔ key0 ∈ (ri \ datakeys(key, n, ri)) ⊖ ro) ∧ (key0 ∈ (ri ⊖ ro) \ datakeys(key, n, ri) → ((ri ⊖ ro) \ datakeys(key, n, ri))[key0] = ((ri \ datakeys(key, n, ri)) ⊖ ro)[key0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ key ∈ ro, (key0 ∈ (ri ⊖ ro) \ datakeys(key, n, ri) ↔ key0 ∈ (ri \ datakeys(key, n, ri)) ⊖ ro) ∧ (key0 ∈ (ri ⊖ ro) \ datakeys(key, n, ri) → ((ri ⊖ ro) \ datakeys(key, n, ri))[key0] = ((ri \ datakeys(key, n, ri)) ⊖ ro)[key0])

Proof step 5 from proof replay-nonorphans-trunc (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information