Can anyone explain why a + b = c in the first line of working?

[misty abyss]

Title.

[wintry cradle]

From 0<a<b<c we get that a+b<2c

Since c|a+b,a+b = k*c

then we got k*c<2c

k<2

and from k>=0,a+b≠0,so k = 1

then a+b=c