intuition.
apply list_choice in H0.
destruct H0.
exists (y <-$ c2; x y).
intuition.
unfold marginal_l.
dist_inline_first.
dist_irr_r.
specialize (H0 x0); intuition.
eapply H0.
unfold marginal_r.
dist_inline_first.
dist_skip.
specialize (H0 x0); intuition.
apply H2.
repeat simp_in_support.
specialize (H0 x0); intuition.
intuition.
eapply (EqDec_dec _).
apply (x <-$ c1; y <-$ c2; z <-$ f2 y; ret (x, z)).
Qed.

Theorem comp_spec_irr_l :
forall (A B C : Set){eqda : EqDec A}{eqdb : EqDec B}{eqdc : EqDec C}(c1 : Comp A)(c2 : Comp B)(f1 : A -> Comp C) P,
well_formed_comp c1 ->
(forall a, In a (getSupport c1) -> comp_spec P (f1 a) c2) ->
comp_spec P (Bind c1 f1) c2.