intuition.
eapply (eqRat_ratAdd_same_r (evalDist c true)).
symmetry.
rewrite ratAdd_comm.
rewrite ratSubtract_ratAdd_inverse_2.
specialize (@evalDist_lossless _ c); intuition.
rewrite <- H1.
clear H1.
eapply evalDist_bool_support.
intuition.
intuition.
eapply evalDist_le_1.
Qed.

Theorem rndBool_bind :
forall
(f : bool -> Comp bool),
Pr[b <-$ {0, 1}; f b] == (1 / 2) * Pr[f true] + (1 / 2) * Pr[f false].