# How to understand the counterexample constructed in the PRP/PRF switching lemma towards the standard proof?

I'm reading a paper Code-Based Game-Playing Proofs and the Security of Triple Encryption , which indicates an error on the standard proof of the PRP/PRF switching lemma using the conditional probability in its chapter 2.

In the standard proof, it defines COLL and DIST events, which COLL means the adversary A asks distinct queries to the oracle and gets the same return, DIST is the complementary event. which makes $$Pr[A^{\pi}\Rightarrow 1]=Pr[A^{\rho }\Rightarrow 1|DIST]$$.

Then the author constructed an counterexample of this equality, which event DIST is true for $$(\rho(0),\rho(1))=(0,0),(0,1),(1,0)$$, but I can't understand why the event $$(0,0)$$ are DIST. Is the adversary A asks distinct queries to the oracle and gets the same return, means a COLL?

Here is an excerpt from the relevant part of the paper below.

but I can't understand why the event $$(\rho(0),\rho(1))=(0,0)$$ is DIST
Because the adversary queries its oracle at 0, gets the answer $$\rho(0)=0$$, and halts. It does not query its oracle at input 1, therefore it never observes a repeated oracle output.