Loosing information in decimation - without aliasing We sample each other sample (01010101). Now say we have a signal - that is inside the original sample which has the pattern of (010-1). 
Decimation gives us 000 for this sub-signal. 
How to prove this is an example of aliasing? Or why else do we have lost information?
The whole point of aliasing and the sampling theoreme is that you cannot (generally) know what an aliased signal was, as you cannot represent infinite bandwidth using finite infornation.

If you have extra knowledge of the input signal (eg that DC is not possible, then you might deduce what a string of 1-1-1 was originally.