cat(h:t, u:v) = h:(u:(cat(t, v)))There are many counterexamples. How about h = 1, t = [2], u = 3 and v = [4]. The left-hand side of the equation is
cat(1:[2], 3:[4]) = cat([1,2], [3,4]) = [1,2,3,4]. from the definition of what cat doesThe right-hand side of the equation is
1:(3:(cat([2], [4]))) = 1:(3:([2,4])) from the definition of cat = 1:[3,2,4] since 3:[2,4] = [3,2,4] = [1,3,2,4] since 1:[3,2,4] = [1,3,2,4]The two sides are not the same for this example. So they are certainly not always the same.