Section sa_preimage.
Variables A B:Type.
Variable B_J: Join B.
Variable PA: Perm_alg B.
Variable f:A -> B.
Variable f':B -> A.
Hypothesis Hf'_f : forall x, f' (f x) = x.
Hypothesis Hf_f' : join_hom (f oo f').

Lemma f_inj : forall x y : A,  f x = f y -> x = y.