reserve x,x1,x2,x3 for Real;

theorem
  cosh(x/2)=sqrt((cosh(x)+1)/2)
proof
A1: cosh.(x/2)>0 by SIN_COS2:15;
  sqrt((cosh(x)+1)/2) = sqrt((cosh.(2*(x/2))+1)/2) by SIN_COS2:def 4
    .= sqrt((2*(cosh.(x/2))^2 - 1 +1)/2) by SIN_COS2:23
    .= cosh.(x/2) by A1,SQUARE_1:22;
  hence thesis by SIN_COS2:def 4;
end;
