::
In very broad terms:
Weak efficiency = share prices reflect all historical information
Semi-strong efficiency = share prices reflect all historical information + reflect all publicly available information
strong efficiency = share prices reflect all historical information + reflect all publicly available information + reflects all information held privately by the directors
In other words, semi-strong is not JUST publicly information, it is the continuation of the weak (it includes the weak efficiency AND is further expanded by publicly available information).
By the same logic, the strong efficiency (includes the weak efficiency AND the semi-strong efficiency AND is once again expanded by the privately held information).
If semi-strong efficiency is broken, the the strong efficiency must be as well!