theorem Th11:
  a1:=len f1 = a2:=len f2 implies a1 = a2 & f1 = f2
proof
A1: <*a1,f1*>.1 = a1 & <*a1,f1*>.2 = f1;
A2: <*a2,f2*>.1 = a2 & <*a2,f2*>.2 = f2;
  assume a1:=len f1 = a2:=len f2;
  hence thesis by A1,A2,XTUPLE_0:3;
end;
