"To avoid a conflict between the TCAS'RA and the ATC command, I think the ATC-man should has a Rule , which should be the same as the TCAS's rule.
It is, when a conflict seen on the Radar display, the ATC man should order the East-West flying aircraft to climb, the North-South flying aircraft to descend."
No - what everyone should do is exactly what the rules say they should do, & the rules should be clear & unambiguous. Uberlingen defined that as a problem; sadly people died before it was properly understood that there were different interpretations around the planet. What does not need to happen now is people making it up as they go along - read the book, follow the rules.