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Proof step 2 from proof replay-orphans-trunc (previous step)

key ∈ ro ⊦ (ri \ datakeys(key, n, ri)) ⊖ ro = ri ⊖ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
key ∈ ro ⊦ # ro = 0, ro = ∅, (ri \ datakeys(key, n, ri)) ⊖ ro = ri ⊖ ro

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ks ≠ ∅ → # ks ≠ 0; (forward) from specification set-basic[node-index]%ne-01: ⊦ key ∈ ks → ks ≠ ∅; (forward) from specification set-basic[node-index]