Are you asking how Hayek's philosophy came to be proven in the real world in the 1900s? If so, it is very difficult to actually prove that Hayek was right. His philosophy's validity is a matter of personal opinion.
For example, in the US today, many followers of Hayek believe that his theory is being proven. They believe that our rights are being gradually taken away as the government gets more and more involved in the economy. They believe that the regulations that the government imposes on things like pollution and worker safety are slowly eroding our right to property.
However, no country has actually gone all the way to becoming socialist in the manner that Hayek says will happen. Believers in his theories can say that the US will one day become socialist and lack freedoms, but there is no real evidence of a country that already has lost its freedom through gradual government intervention (as opposed to losing it through complete revolution the way the USSR did).