proposition: Theorem pre_strong_hypothesis_rule {A1 A2 : ord_choiceType} {S1 S2 : choiceType} {d1 : FrStP S1 A1} {d2 : FrStP S2 A2} : forall (pre : S1 * S2 -> Prop) post, (forall st1 st2, pre (st1, st2)) -> (⊨ ⦃ (fun st => True ) ⦄ d1 ≈ d2 ⦃ post ⦄) -> (⊨ ⦃ pre ⦄ d1 ≈ d2 ⦃ post ⦄).
proof: Proof. move => pre post Hpre Hjudg. by apply (pre_weaken_rule (fun st => True) _). Qed.
imports: Coq(RelationClasses Morphisms Utf8) Mon(SPropMonadicStructures SpecificationMonads MonadExamples SPropBase FiniteProbabilities) Relational(OrderEnrichedCategory OrderEnrichedRelativeMonadExamples Commutativity GenericRulesSimple) mathcomp(all_ssreflect all_algebra reals distr realsum finmap.set finmap.finmap xfinmap) Crypt(Axioms ChoiceAsOrd SubDistr Couplings Theta_dens Theta_exCP LaxComp FreeProbProg RelativeMonadMorph_prod StateTransformingLaxMorph choice_type)