(related to Proposition: Double Summation)
The rule of double summation \[\sum_{i=1}^n\sum_{j=1}^m a_{ij}=\sum_{j=1}^m\sum_{i=1}^n a_{ij}\] is a direct corollary from the general associativity law and is valid for summing of elements of any commutative semigroup \(a_i,a_j\in(S, +)\).
