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 Th7:
  not a _|_ c implies not a+b _|_ c or not (1_F+1_F)*a+b _|_ c
proof
  set 1F = 1_F;
  assume
A1: not a _|_ c;
  assume
A2: not thesis;
  then (1F*a+1_F*a)+b _|_ c by VECTSP_1:def 15;
  then (a+1F*a)+b _|_ c;
  then (a+a)+b _|_ c;
  then a+(a+b) _|_ c by RLVECT_1:def 3;
  hence contradiction by A1,A2,Th4;
end;
