reserve SAS for Semi_Affine_Space;
reserve a,a9,a1,a2,a3,a4,b,b9,c,c9,d,d9,d1,d2,o,p,p1,p2,q,r,r1,r2,s,x, y,t,z
  for Element of SAS;

theorem Th8:
  a<>b & p,q // a,b & a,b // r,s implies p,q // r,s
proof
  assume that
A1: a<>b and
A2: p,q // a,b and
A3: a,b // r,s;
  a,b // p,q by A2,Th6;
  hence thesis by A1,A3,Def1;
end;
