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 Th11:
  f just_once_values y implies f " {y} = {f <- y}
proof
  assume
A1: f just_once_values y;
  then consider x such that
A2: {x} = f " {y} by Th6;
A3: x in f " {y} by A2,ZFMISC_1:31;
  then f.x in {y} by FUNCT_1:def 7;
  then
A4: f.x = y by TARSKI:def 1;
  x in dom f by A3,FUNCT_1:def 7;
  hence thesis by A1,A2,A4,Def3;
end;
