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;

theorem Th5:
  f just_once_values y implies y in rng f
proof
  assume f just_once_values y;
  then card Coim(f,y) = 1;
  then rng f meets {y} by CARD_1:27,RELAT_1:138;
  then consider x being object such that
A1: x in rng f /\ {y} by XBOOLE_0:4;
  x in {y} by A1,XBOOLE_0:def 4;
  then y = x by TARSKI:def 1;
  hence thesis by A1,XBOOLE_0:def 4;
end;
