Cell Mitosis dp - proof for even n

How can you prove that the cost to reach n (even) from n+1 is always greater ?

take this array indexing
1 2 3 4 5 6 7 8 9

To reach 8, you can reach via 4,7,9
To reach 9, you can reach via 8,10.
Target 8:
Reaching via 8->9->8 or 10->9->8 is difficult than 4->8 or 7->8.
Think recursively in the case 10->9->8, to reach 10 apply the same logic. It is not easy to get but you’ll!

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