= Normal benign subgroup quotient embedding
{title2=$G/N\hookrightarrow P$}
If $N\triangleleft G$ is a <benign subgroup>, use its witness $N=G\cap L$ inside a <finitely presented group>. Enumerate words on the generators of $L$, together with proofs that each equals a substituted word on the generators of $G$. This enumerates exactly the null words of $G/N$, giving a <recursive presentation of a group>. The <Higman embedding theorem> then embeds the finitely generated quotient in a finitely presented group.
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