proposition: Lemma CTXT_EVAL_equiv_false: CTXT_EVAL_pkg_ff ∘ EVAL_SAMP_pkg ∘ SAMP Ciph_N false ≈₀ CTXT_EVAL_pkg_ff ∘ EVAL false.
proof: Proof. apply: eq_rel_perf_ind_eq. simplify_eq_rel m. all: apply rpost_weaken_rule with eq; last by move=> [? ?] [? ?] []. 2: ssprove_code_simpl. 2: rewrite cast_fun_K. 2: ssprove_code_simpl. 2: ssprove_code_simpl_more. 2: ssprove_sync_eq=> S. 2: ssprove_sync_eq=> H1. 2: ssprove_sync_eq=> Tinv. 2: rewrite domm_fset_to_chset. all: by apply: rreflexivity_rule. Qed.
imports: Relational(OrderEnrichedCategory GenericRulesSimple) mathcomp(all_ssreflect all_algebra reals distr realsum ssrnat ssreflect ssrfun ssrbool ssrnum eqtype choice seq) Mon(SPropBase) Crypt(Axioms ChoiceAsOrd SubDistr Couplings UniformDistrLemmas FreeProbProg Theta_dens RulesStateProb pkg_core_definition choice_type pkg_composition pkg_rhl Package Prelude) extructures(ord fset fmap) Equations(Equations)