reserve f for Function;
reserve p,q for FinSequence;
reserve A,B,C for set,x,x1,x2,y,z for object;
reserve k,l,m,n for Nat;
reserve a for Nat;
reserve D for non empty set;
reserve d,d1,d2,d3 for Element of D;

theorem Th30:
  p just_once_values x iff len(p - {x}) = len p - 1
proof
  thus p just_once_values x implies len(p - {x}) = len p - 1
  by FINSEQ_3:59;
  assume len(p - {x}) = len p - 1;
  then len p + -1 = len p - card(p " {x}) by FINSEQ_3:59
    .= len p + - (card (p"{x}));
  hence thesis;
end;
