Mathematical notation for Summing with if's

Question

I'm trying to write a mathematical notation for the following logic

total = 0
Co = 10

for element in elementlist:
    if element contains A:
        Ci = A
    elif element contains B:
        Ci = B
    else:
        Ci = Po
    total += Co - Ci

Here is what I have come up with but I'd like some extra eyes.

Thanks so much!

Answer 1

$$total = \sum_{i\in A}\left( C_0-C_i\right)+ \sum_{i\in B}\left( C_0-C_i\right)+ \sum_{i\in C}\left( C_0-C_i\right)$$ $$ = C_0|A|-\sum_{i\in A}C_i+ C_0|B|-\sum_{i\in B}C_i+ C_0|C|-\sum_{i\in C}C_i$$ $$ = C_0|A|+ C_0|B|+ C_0|C|-\sum_{i\in A}C_i-\sum_{i\in B}C_i-\sum_{i\in C}C_i$$ $$ = C_0\left(|A|+ |B|+ |C|\right)-\left(\sum_{i\in A}C_i+\sum_{i\in B}C_i+\sum_{i\in C}C_i\right)$$ $$ = C_0\left(|A|+ |B|+ |C|\right)-\sum_{i\in A\cup B\cup C}C_i$$