reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;
reserve m,n,k for Nat, R for Relation;

theorem Th93:
  for f being Function, a, b being object holds (f +* (a .--> b)).a =
  b
proof
  let f be Function, a, b be object;
  a in dom (a .--> b) by TARSKI:def 1;
  hence (f +* (a .--> b)).a = (a .--> b).a by FUNCT_4:13
    .= b by FUNCOP_1:72;
end;
