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The butterfly spread satisfies the inequality
c(X1) - 2c(X2) + c(X3) >= 0
Where call strikes satisfy X1<X2<X3 and X2 - X1 = X3 - X2.
There is a “proof” that was provided here https://quant.stackexchange.com/a/32609/66878. However the proof is missing many steps and serves more as an outline.
Could anyone elaborate on the proof or provide their own in full detail?
Thanks so much,