diff --git a/draft-irtf-cfrg-vdaf.md b/draft-irtf-cfrg-vdaf.md
index 376d9f55..b9099119 100644
--- a/draft-irtf-cfrg-vdaf.md
+++ b/draft-irtf-cfrg-vdaf.md
@@ -2174,15 +2174,9 @@ its measurement such that the verifier will only accept the measurement once
 all proofs have been thoroughly verified. Notably, several proofs using a smaller
 field can offer the same level of soundness as a single proof using a large field.
 
-To generate these proofs for a specific measurement, the prover can call
-`Flp.prove` multiple times, using different sets of prover/joint randomnesses.
-Then the shares of these proofs are distributed to the verifier. Subsequently,
- the verifier utilizes `Flp.query` to compute one share of verifier message
- for each proof share, based on the measurement, the proof share, the joint
- randomness, and unique query randomness. Finally, the
-verifier runs `Flp.decide` on each verifier message to make a decision. The
-validity of the measurement is determined through the logical conjunction
-of all Boolean outputs yielded by `Flp.decide`.
+To generate these proofs for a specific measurement, the prover calls
+`Flp.prove` multiple times, each time using an independently generated prover and joint randomness string.
+The verifier checks each proof independently, each time with an independently generated query randomness string. It accepts the measurement only if all the decision algorithm accepts on each proof.
 
 
 ## Construction {#prio3-construction}