reserve a,b,c for positive Real,
  m,x,y,z for Real,
  n for Nat,
  s,s1,s2,s3,s4,s5 for Real_Sequence;

theorem
  b/a+a/b>=2
proof
  (a-b)^2>=0 by XREAL_1:63;
  then a^2-2*a*b+b^2+2*a*b>=0+2*a*b by XREAL_1:7;
  then (a^2+b^2)/(a*b)>=(2*(a*b))/(1*(a*b)) by XREAL_1:72;
  then
A1: (a^2+b^2)/(a*b)>=2/1 by XCMPLX_1:91;
  b/a+a/b = (b*b)/(a*b)+a/b by XCMPLX_1:91
    .= (b*b)/(a*b)+(a*a)/(a*b) by XCMPLX_1:91
    .= (b^2+a^2)/(a*b);
  hence thesis by A1;
end;
