theorem Th2:
  x>0 implies x #R (1/2)=sqrt x
proof
  assume
A1: x>0;
  then
A2: x #R (1/2)>0 by PREPOWER:81;
  x = x #R ((1/2)*2) by A1,PREPOWER:72
    .=x #R (1/2) #R 2 by A1,PREPOWER:91
    .=(x #R (1/2)) #Q 2 by A1,PREPOWER:74,81
    .=(x #R (1/2)) to_power 2 by A1,POWER:44,PREPOWER:81
    .=(x #R (1/2))^2 by POWER:46;
  hence thesis by A1,A2,SQUARE_1:def 2;
end;
