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<>0.F & Tern(a,x,b) = Tern(a,x9,b) implies x=x9
proof
  assume that
A1: a<>0.F and
A2: Tern(a,x,b) = Tern(a,x9,b);
  set c = Tern(a,x,b);
A3: Tern(a,x,b) = Tern(0.F,x,c) by Def5;
  Tern(a,x9,b) = Tern(0.F,x9,c) by A2,Def5;
  hence thesis by A1,A3,Def5;
end;
