
theorem
not F_Real is SplittingField of X^2-2
proof
set F = FAdj(F_Rat,{2-Root(2)});
now assume A: F_Real is SplittingField of X^2-2;
  X^2-2 splits_in F by 2split,FIELD_8:def 1; then
  F_Real == F by A,FIELD_8:def 1; then
  F_Real is Subfield of F by FIELD_7:def 2; then
  the carrier of F_Real c= the carrier of F by EC_PF_1:def 1;
  hence contradiction by nnn;
  end;
hence thesis;
end;
