reserve a,b,c,d,a9,b9,c9,d9,y,x1,u,v for Real,
  s,t,h,z,z1,z2,z3,s1,s2,s3 for Complex;

theorem Th12:
  y^2 = a implies y = sqrt a or y = -sqrt a
proof
  assume
A1: y^2 = a;
  then
A2: a >= 0 by XREAL_1:63;
  Polynom(1,0,-a,y) =0 by A1;
  then y=(-0+sqrt delta(1,0,-a))/(2*1) or y=(-0-sqrt delta(1,0,-a))/(2*1) by A2
,POLYEQ_1:5;
  then y=(sqrt (4*a))/2 or y=(0-sqrt (4*a))/2;
  then y= sqrt a * 2 /2 or y=(-(2 * sqrt a))/2 by A2,SQUARE_1:20,29;
  hence thesis;
end;
