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
  f is one-to-one & y in rng f implies (f").y = f <- y
proof
  assume that
A1: f is one-to-one and
A2: y in rng f;
  consider x being object such that
A3: x in dom f & f.x = y by A2,FUNCT_1:def 3;
  f just_once_values y by A1,A2,Th8;
  then x = f <- y by A3,Def3;
  hence thesis by A1,A3,FUNCT_1:32;
end;
