proposition: Lemma repr_bind : ∀ {A B : choiceType} (p : raw_code A) (f : A → raw_code B), repr (bind p f) = bindrFree (repr p) (λ a, repr (f a)).
proof: Proof. intros A B p f. induction p in f |- *. - cbn. reflexivity. - simpl. auto. - simpl. f_equal. extensionality x. auto. - simpl. f_equal. extensionality x. f_equal. extensionality y. auto. - simpl. f_equal. extensionality x. auto. Qed.
imports: Coq(Utf8) Relational(OrderEnrichedCategory OrderEnrichedRelativeMonadExamples) mathcomp(ssrnat ssreflect ssrfun ssrbool ssrnum eqtype choice reals distr seq all_algebra fintype realsum) extructures(ord fset fmap) Mon(SPropBase) Crypt(Prelude Axioms ChoiceAsOrd SubDistr Couplings RulesStateProb UniformStateProb UniformDistrLemmas StateTransfThetaDens StateTransformingLaxMorph choice_type pkg_core_definition pkg_notation pkg_tactics pkg_composition pkg_heap) Equations.Prop.DepElim Equations(Equations) Crypt(FreeProbProg)