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 just_once_values y implies Im(f, f<-y) = {y}
proof
  assume
A1: f just_once_values y;
  then f <- y in dom f by Def3;
  hence Im(f,f <- y) = {f.(f <- y)} by FUNCT_1:59
    .= {y} by A1,Def3;
end;
