Proof of using a literal from known set, inside a computed formula
In Crypto 94, Cramer, Damgård and Schoenmakers proposed Proofs of Partial Knowledge and Simplified Design of Witness Hiding Protocols with abstract below:
Suppose we are given a proof of knowledge $P$ in which a prover demonstrates that he knows a solution to a given problem instance. Suppose also that we have a secret sharing scheme $S$ on $n$ participants. Then under certain assumptions on $P$ and $S,$ we show how to transform $P$ into a witness indistinguishable protocol, in which the prover demonstrates knowledge of the solution to some subset of $n$ problem instances out of a collection of subsets defined by $S.$
For example, using a threshold scheme, the prover can show that he knows at least $d$ out of $n$ solutions without revealing which $d$ instances are involved. If the instances are independently generated, we get a witness hiding protocol, even if $P$ did not have this property.
Our results can be used to efficiently implement general forms of group oriented identification and signatures. Our transformation produces a protocol with the same number of rounds as $P$ and communication complexity $n$ times that of $P.$ Our results use no unproven complexity assumptions.
The authors also state:

Our techniques are to some extent related to those of De Santis et al. The models are quite different, however: They consider non-interactive proofs of membership, while we consider interactive proofs of knowledge.

The paper is available here