reserve F for Field;
reserve S for SymSp of F;
reserve a,b,c,d,a9,b9,p,q,r,s,x,y,z for Element of S;
reserve k,l for Element of F;

theorem Th9:
  a<>0.S & b<>0.S implies ex p st not p _|_ a & not p _|_ b
proof
  assume that
A1: a<>0.S and
A2: b<>0.S;
  consider a9 such that
A3: not a9 _|_ a by A1,Def1;
  now
    consider b9 such that
A4: not b9 _|_ b by A2,Def1;
    assume
A5: a9 _|_ b;
    now
      assume b9 _|_ a;
      then ( not a9+b9 _|_ a)& not a9+b9 _|_ b by A3,A5,A4,Th8;
      hence thesis;
    end;
    hence thesis by A4;
  end;
  hence thesis by A3;
end;
