Uniquely removable subsequences
Haskell, 90 84 bytes

a%[]=[a]
(t:z)%x@(s:y)=[a|a&lt;-z%y,t==s]++[t:s|s&lt;-z%x]
_%_=[]
((all=&lt;&lt;(==).head).).(%)


Construct the list of all possible subtracted sequences nondeterministically and checks whether they are all equal.

Usage: 

*Main&gt; mapM_(\(a,b)-&gt;let r=(((all=&lt;&lt;(==).head).).(%)) a b in putStrLn$concat[show a," ",show b," -&gt; ",show r]) [([],[]), ([0,3],[]), ([1,0,1],[1]), ([0,2],[0,2]), ([2,2,1,1,2,2,2],[2,1]), ([4,2,2,4,4,6,5],[4,5]), ([10,5,10,10,5,10],[10,5,10]), ([4,2,2,4,4,6,5],[2,4,5]), ([1,1,1,0,0,0,1,1,1,0],[1,0,1,1]), ([0,1,0,0,0,0,1,1,0,1],[1,0,1,1]), ([0,4,0,0,4,1,4,2,2],[0,0,0,1,4]), ([0,2,2,25,0,2,2,26,0,0,2],[2,0,0,0,2]), ([1,1,1,3,2,1,3,2,2,3,3,2],[1,1,2,3,2]), ([0,3,2,0,1,3,2,0,0,0,3,2],[0,1,2,0,3]), ([5,7,2,7,7,1,7,7,5,2,7,7,5,2,2,7,5],[2,7,5,7,7,2]), ([5,4,0,5,4,5,4,1,0,4,2,1,1,2,4,4,0,2,2,1],[4,0,1,1,2,1]), ([0,1,4,0,1,4,0,1,5,1,4,4,2,0,0,1,1,1,2,4],[0,1,0,0,2,0,1,4])]
[] [] -&gt; True
[0,3] [] -&gt; True
[1,0,1] [1] -&gt; False
[0,2] [0,2] -&gt; True
[2,2,1,1,2,2,2] [2,1] -&gt; True
[4,2,2,4,4,6,5] [4,5] -&gt; False
[10,5,10,10,5,10] [10,5,10] -&gt; False
[4,2,2,4,4,6,5] [2,4,5] -&gt; True
[1,1,1,0,0,0,1,1,1,0] [1,0,1,1] -&gt; True
[0,1,0,0,0,0,1,1,0,1] [1,0,1,1] -&gt; False
[0,4,0,0,4,1,4,2,2] [0,0,0,1,4] -&gt; True
[0,2,2,25,0,2,2,26,0,0,2] [2,0,0,0,2] -&gt; True
[1,1,1,3,2,1,3,2,2,3,3,2] [1,1,2,3,2] -&gt; False
[0,3,2,0,1,3,2,0,0,0,3,2] [0,1,2,0,3] -&gt; False
[5,7,2,7,7,1,7,7,5,2,7,7,5,2,2,7,5] [2,7,5,7,7,2] -&gt; False
[5,4,0,5,4,5,4,1,0,4,2,1,1,2,4,4,0,2,2,1] [4,0,1,1,2,1] -&gt; False
[0,1,4,0,1,4,0,1,5,1,4,4,2,0,0,1,1,1,2,4] [0,1,0,0,2,0,1,4] -&gt; True


Thanks to @Zgarb for saving 6 bytes!