proposition: Lemma bijective_f : ∀ m, bijective (f m).
proof: Proof. intro m. pose proof bijective_expgn as bij. destruct bij as [d hed hde]. eexists (λ '(x,y), (d x, d ((otf m)^-1 * y))). - intros [? ?]. simpl. rewrite hed. f_equal. rewrite mulgA. rewrite mulVg. rewrite mul1g. apply hed. - intros [x y]. simpl. rewrite hde. f_equal. rewrite hde. rewrite mulgA. rewrite mulgV. rewrite mul1g. reflexivity. Qed.
imports: Relational(OrderEnrichedCategory GenericRulesSimple) mathcomp(all_ssreflect all_algebra reals distr realsum fingroup.fingroup solvable.cyclic prime ssrnat ssreflect ssrfun ssrbool ssrnum eqtype choice seq) Mon(SPropBase) Crypt(Axioms ChoiceAsOrd SubDistr Couplings UniformDistrLemmas FreeProbProg Theta_dens RulesStateProb UniformStateProb pkg_core_definition choice_type pkg_composition pkg_rhl Package Prelude AsymScheme) Coq(Utf8) extructures(ord fset fmap) Equations(Equations)