reserve AFV for WeakAffVect;
reserve a,a9,b,b9,c,d,p,p9,q,q9,r,r9 for Element of AFV;
reserve AFV for WeakAffSegm;
reserve a,b,b9,b99,c,d,p,p9 for Element of AFV;

theorem Th7:
  a,b // p,p9 & a,b // b,c & a,p // p,b & a,p9 // p9,b implies a=c
proof
  assume that
A1: a,b // p,p9 and
A2: a,b // b,c and
A3: a,p // p,b and
A4: a,p9 // p9,b;
  p,b // a,p by A3,Th2;
  then p,b // p,a by Th3;
  then
A5: b,p // p,a by Th4;
  p9,b // a,p9 by A4,Th2;
  then p9,b // p9,a by Th3;
  then
A6: b,p9 // p9,a by Th4;
  b,a // p,p9 by A1,Th4;
  then a,a // a,c by A2,A5,A6,Def1;
  then a,c // a,a by Th2;
  hence thesis by Def1;
end;
