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 Th3:
  not a _|_ b & c+a _|_ b implies not c _|_ b
proof
  assume that
A1: not a _|_ b and
A2: c+a _|_ b;
  assume not thesis;
  then (-1_F)*c _|_ b by Def1;
  then -c _|_ b by VECTSP_1:14;
  then -c+(c+a) _|_ b by A2,Def1;
  then (c+(-c))+a _|_ b by RLVECT_1:def 3;
  then 0.S+a _|_ b by RLVECT_1:5;
  hence contradiction by A1,RLVECT_1:4;
end;
