 reserve i,j,k,k0,m,n,N for Nat;
 reserve x,y for Real;
 reserve p for Prime;

theorem ::LtSqrt:
  x^2 < y implies x < sqrt y
  proof
    assume A1: x^2 < y;
    A2: x <= |.x.| by COMPLEX1:76;
    |.x.|^2 < y by A1,COMPLEX1:75;
    then sqrt |.x.|^2 < sqrt y by SQUARE_1:27;
    then |.x.| < sqrt y by COMPLEX1:46,SQUARE_1:22;
    hence thesis by A2,XXREAL_0:2;
  end;
