Certain FieldDefinition expressions don't work, such as

var index = 1;
Builders<Person>.Update.Inc(x => x..Pets[index].Age, 1);

This will break because we have a member binding to a display class as opposed to a constant where index exists. If you are using a constant instead of a variable as an index, then there isn't a problem.

Workaround

Instead of using a lambda expression, you can use a string.

var index = 1;
var fieldName = string.Format("Pets.{0}.Age", index);
Builders<Person>.Update.Inc(fieldName, 1);

*Note that any members that have been mapped to alternate names will still get mapped. This just lacks refactoring support.