Strange Summation Identity – Mathematics Stack Exchange

I was looking at the Summation wikipedia(https://en.m.wikipedia.org/wiki/Summation) and found this rather strange identity:
$$
sum_{kleq jleq ileq n} a_{i,j}=sum_{i=k}^nsum_{j=k}^i a_{i,j}=sum_{j=k}^nsum_{i=j}^n a_{i,j}=sum_{j=0}^{n-k}sum_{i=k}^{n-j} a_{i+j,i}
$$

Can someone please explain me what the term before the first equal to sign mean and provide me with a proof of above?