Common use of Proof sketch Clause in Contracts

Proof sketch. Assume that there is an algorithm A that achieves approximate agreement when n 3f . We partition the n nodes into three (non-empty) sets of size at most f : V0, V1, and Vb. Nodes in set V0 are correct and have input 0, and, similarly, nodes in set V1 are correct and have input 1. The nodes in Vb are corrupted, and, similarly to Theorem 17.13, they support the input value of each correct node. This way, because of correct-range validity, nodes in V0 output 0, and nodes in V1 output 1, which breaks ε-agreement for any ε < 1.

Proof sketch. Assume that there is an algorithm A that achieves approximate agreement when n 3f . We partition the n nodes into three (non-empty) sets of size at most f : V0, V1, and Vb. Nodes in set V0 are correct and have input 0, and, similarly, nodes in set V1 are correct and have input 1. The nodes in Vb are corrupted, and, similarly to Theorem 17.1317.11, they support the input value of each correct node. This way, because of correct-range validity, nodes in V0 output 0, and nodes in V1 output 1, which breaks ε-agreement for any ε < 1.