reserve F for non empty TernaryFieldStr;
reserve a,b,c for Scalar of F;
reserve F for Ternary-Field;
reserve a,a9,b,c,x,x9,u,u9,v,v9,z for Scalar of F;

theorem
  a<>a9 & Tern(u,a,v) = Tern(u9,a,v9) & Tern(u,a9,v) = Tern(u9,a9,v9)
  implies u=u9 & v=v9
proof
  assume that
A1: a<>a9 and
A2: Tern(u,a,v) = Tern(u9,a,v9) and
A3: Tern(u,a9,v) = Tern(u9,a9,v9);
  u = u9 by A1,A2,A3,Def5;
  hence thesis by A2,Def5;
end;
