proposition: Lemma pmulr_me (x y : R) : 0 <= y -> (0 < y * x) -> (0 < x).
proof: Proof. rewrite le0r => /orP[/eqP->|]. - by rewrite GRing.mul0r order.Order.POrderTheory.ltxx. - intros. by rewrite -(pmulr_rgt0 x b). 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 pkg_semantics pkg_lookup pkg_advantage pkg_invariants pkg_distr) Equations.Prop.DepElim Equations(Equations) Crypt(FreeProbProg)