Let's parse that assertion:

- Provide, if you will, the teaching of the four cardinals that they are teaching without any authorization.

- Provide, if you will, the order, directive, or command of lawful authority which the four cardinals are defying.

- Since the cardinals asked for clarification in their request citing specific instances of prior teaching, and since the Holy Father has not declared publicly which of competing interpretations - if any - are acceptable, provide if you will a description of the "union" with the Petrine Office would require.