(*Examples of quantifier elimination, using "CylindricalDecomposition"*)

CylindricalDecomposition[Exists[x,a x^2+b x+c==0&&a>0],{x,a,b,c}]

CylindricalDecomposition[ForAll[x,Exists[y,Exists[z,z^2+4x+y x z^3≤x^2+y^5-x+1]]],{x,y,z}]

CylindricalDecomposition[Exists[y,Exists[z,z^2+4x+y x z^3≤x^2+y^5-x+1]],{x,y,z}]

CylindricalDecomposition[Exists[y,x+y^2≤5],{x,y}]