European vanilla Call option with strike price, Other Engineering

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Let C(K) denote a European vanilla Call option with strike price K. Assume that all options are identical except for strike price, and strike prices satisfy K1
Question 1:
What are the no-arbitrage lower bound, and the no-arbitrage upper bound, of the vertical spread C(K1)-C(K2)?

Question 2:
Derive the functional relationship between the no-arbitrage values of the two vertical spreads, C(K1)-C(K2) and C(K2) - C(K3)

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