proposition: Lemma Invariant_inv_conj : ∀ L₀ L₁ inv sinv, Invariant L₀ L₁ inv → SemiInvariant L₀ L₁ sinv → Invariant L₀ L₁ (inv ⋊ sinv).
proof: Proof. intros L₀ L₁ inv sinv [his hie] [hss hse]. split. - intros s₀ s₁. specialize (his s₀ s₁). destruct his. split. + intros []. eauto. + intros [] ℓ v h₀ h₁. split. all: eauto. - split. all: eauto. 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) Equations.Prop.DepElim Equations(Equations) Crypt(FreeProbProg)