Constraint about encrypted values Let V = $[x_1,\ldots ,x_n]$  be a binary vector of length $n$, and let $E(V)$ be the entrywise encryption of this vector.

Suppose I want to give to another player, $E(V)$, but also let him have the ability to verify that the plain vector contains  m values that are equal to 1, and they are  consecutive.

For example, n=5,m=2:

Valid V = 0,1,1,0,0;
Not valid V = 0,1,0,1,0.

Note that: If the requirement was without the consecutive property, I've just used an homomorphic encryption. (to see if the multiplication of the values are equal to the encryption of $m$).
To capture value/position relations, a "sequence polynomial representation" was suggested, in the context of proving properties of DNA. Self-citing: IACR preprint 2008/357. This technique could apply here in case of ElGamal ciphertext, that could be proven with Schnorr-like responses. The major idea remains to re-state "consecutive" as a property of "characteristic polynomial", that (I believe) is doable. Hamiltonicity test (2008/363) could be another example.