I'm having hard time finding the Loop invariant, then using that to prove the initialization,maintenance, and termination phase. plz explain every step on the way I'm struggling with it. Thanks.

01 def head (Q): 02 return 0 [0] 32 33 L + S = S + return s R 03 def tail (0): 04 return 0[1:] Here is how head, tail, and mergesort. 05 def mergesort (U): 06 if u if U == [1 or tail() = (1 : return U else: L = [] R = [] while True: if U = (1 : break else: L = 1 + [head (U)] U = tail(U) if u == U: break else: R = R + [head (U)] U = tail (U) La mergesert (L) R = mergesert (R) S = [] while L != [] and R != (: if head (L)