Top/Data structures/Lists/Equations/Answer-equation-4

Answer to Question equation-4

Here are the equations for reference. 
  (cat.1)   cat([],  B) = B
  (cat.3)   cat(h:t, B) = h:cat(t, B)
Evaluation is as follows. 
  cat([1,2,3], [4,5,6]) = cat(1:[2,3], [4,5,6])
                        = 1:cat([2,3], [4,5,6])       by (cat.3)
                        = 1:cat(2:[3], [4,5,6])
                        = 1:(2:cat([3], [4,5,6]))     by (cat.3)
                        = 1:(2:cat(3:[], [4,5,6]))
                        = 1:(2:(3:cat([], [4,5,6])))  by (cat.3)
                        = 1:(2:(3:[4,5,6]))           by (cat.1)
                        = 1:(2:([3,4,5,6]))
                        = 1:([2,3,4,5,6])
                        = [1,2,3,4,5,6]