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The midpoint butterfly buys half a call at each outer strike and sells one at the middle strike. Convexity of $K\mapsto (S-K{)}^{+}$ makes its terminal payoff nonnegative. A violation of the displayed price inequality makes its cost negative and creates arbitrage. The payoff is triangular between the outer strikes and zero elsewhere.

A contingent claim is replicated when an admissible self-financing portfolio has exactly its terminal payoff. In the absence of arbitrage, two replicating strategies for the same payoff have the same initial cost.