After the th answer has been received, an assistant carries out the following instructions:
1. Save the answer in memory and put  = 0.

2. For  = 1, … , , start up 
(
) for  cycles of calculation.

3. If  has provided not less than  +  − 1 answers, and these answers are equal to the received answers, put  = 1.

4. Report the value of  to .

Supervisor  treats the messages δ and δℜ of  and ℜ according to the following table.

![0_image_0.png](0_image_0.png)

If some communicable TM ℭ has passed the test, then symbol 1 appears in the sequence of messages from the assistant that processes the answers of , and then for some  the first  + - 1 answers of  are equal to the answers of 
. As a result, {ℭ ⊳ ℑ,  } ≤ 
∞ +−1
=1. □