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theory Compositionality(* Title: HOLCF/IOA/meta_theory/Compositionality.thy ID: $Id: Compositionality.thy,v 1.6 2005/09/02 15:24:01 wenzelm Exp $ Author: Olaf Müller *) header {* Compositionality of I/O automata *} theory Compositionality imports CompoTraces begin end
theorem compatibility_consequence3:
[| eA --> A; eB ∧ ¬ eA --> ¬ A |] ==> eA ∨ eB --> A = eA
theorem Filter_actAisFilter_extA:
[| compatible A B; Forall (%a. a ∈ ext A ∨ a ∈ ext B) tr |] ==> Filter (%a. a ∈ act A)·tr = Filter (%a. a ∈ ext A)·tr
theorem compatibility_consequence4:
[| eA --> A; eB ∧ ¬ eA --> ¬ A |] ==> eB ∨ eA --> A = eA
theorem Filter_actAisFilter_extA2:
[| compatible A B; Forall (%a. a ∈ ext B ∨ a ∈ ext A) tr |] ==> Filter (%a. a ∈ act A)·tr = Filter (%a. a ∈ ext A)·tr
theorem compositionality:
[| is_trans_of A1.0; is_trans_of A2.0; is_trans_of B1.0; is_trans_of B2.0; is_asig_of A1.0; is_asig_of A2.0; is_asig_of B1.0; is_asig_of B2.0; compatible A1.0 B1.0; compatible A2.0 B2.0; A1.0 =<| A2.0; B1.0 =<| B2.0 |] ==> (A1.0 || B1.0) =<| (A2.0 || B2.0)