proposition: Lemma r_forget_lhs : ∀ {A B : choiceType} c₀ c₁ (pre : precond) (post : postcond A B) ℓ v, ⊢ ⦃ λ '(s₀, s₁), pre (s₀, s₁) ⦄ c₀ ≈ c₁ ⦃ post ⦄ → ⊢ ⦃ λ '(s₀, s₁), (pre ⋊ rem_lhs ℓ v) (s₀, s₁) ⦄ c₀ ≈ c₁ ⦃ post ⦄.
proof: Proof. intros A B c₀ c₁ pre post ℓ v h. eapply rpre_weaken_rule. - eapply h. - simpl. intros ? ? []. 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 pkg_semantics pkg_lookup pkg_advantage pkg_invariants pkg_distr) Equations.Prop.DepElim Equations(Equations) Crypt(FreeProbProg)