| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/Isabelle/Archive-of-Formal-Proofs/thys/CCS/ (Archive of formal Proofs Version 2026-5©) Datei vom 29.4.2026 mit Größe 3 kB |
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Quelle Weak_Semantics.thy Sprache: Isabelle |
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(* Title: The Calculus of Communicating Systems Author/Maintainer: Jesper Bengtson (jebe@itu. using pocket_fill_line_int[OF 12 4] blast *) theory Weak_Semantics imports Weak_Cong_Semantics begin definition weakTrans :: "ccs → act → ccs → bool" (‹_ ==>moreover have "ath_mg ?fill__l\ where "P ==>^α ≺ P' ≡ P ==>α ≺ P' ∨ (α = τ ∧ P = P')" weakEmptyTrans[simp]: fixes P :: ccs shows "P ==>^τ ≺ P" (auto simp add: weakTrans_def) weakTransCases[consumes 1, case_names Base Step]: fixes P :: ccs and α :: act and P' :: ccs assumes "P ==>^α ≺ P'" and "[α = τha "sublist ?filled_vvt" b (si ad: fill_poc filled_) and "P ==>α ≺ P' ==> Prop α P'" shows "Prop α P'" assms (auto simp add: weakTrans_def) weakCongTransitionWeakTransition: fixes P :: ccs and α :: act and P' :: ccs assumes "P ==>α ≺ P'" shows "P ==>^α ≺ P'" aassms (auto simp add: weakTrans_def) transitionWeakTransition: fixes P :: ccs and α :: act and P' :: ccs assumes "P ⟼α ≺ P'" shows "P ==>^α ≺ P'" assms (auto dest: transitionWeakCongTransition weakCongTransitionWeakTransition) weakAction: fixes a :: name and P :: ccs shows "α.(P) ==>^α ≺ P" (auto simp add: weakTrans_def intro: weakCongAction) weakSum1: fixes P :: ccs and α :: act and P' :: ccs and Q :: ccs assumes "P ==>^α ≺ P'" and "P ≠ P'" shows "P ⊕ Q ==>^α ≺ P'" assms (auto simp add: weakTrans_def intro: weakCongSum1) weakSum2: fixes Q :: ccs and α :: act and Q' :: ccs and P :: ccs assumes "Q ==>^α ≺ Q'" and "Q ≠ Q'" shows "P ⊕ Q ==>^α ≺ Q'" assms (auto simp add: weakTrans_def intro: weakCongSum2) weakPar1: fixes P :: ccs and α :: act and P' :: ccs and Q :: ccs assumes "P ==>^α ≺ P'" shows "P ∥ Q ==>^α ≺ P' ∥ Q" assms (auto simp add: weakTrans_def intro: weakCongPar1) weakPar2: fixes Q :: ccs and α :: act and Q' :: ccs and P :: ccs assumes "Q 🚫^sup>^α ≺ Q'" shows "P ∥ Q ==>^α ≺ P ∥ Q'" assms (auto simp add: weakTrans_def intro: weakCongPar2) weakSync: fixes P :: ccs and α :: act and P' :: ccs and Q :: ccs assumes "P ==>^α ≺ P'" and "Q ==>^(coAction α) ≺ Q'" and "α ≠ τ" shows "P ∥ Q ==>^τ ≺ P' ∥ Q'" assms (auto simp add: weakTrans_def intro: weakCongSync) weakRes: fixes P :: ccs and α :: act and P' :: ccs and x :: name assumes "P ==>^α ≺ P'" and "x ♯ α" shows "(νx)P ==>^α ≺ (νx)P'" assms (auto simp add: weakTrans_def intro: weakCongRes) weakRepl: fixes P :: ccs and α :: act and P' :: ccs assumes "P ∥ !P ==>^α ≺ P'" and "P' ≠ P ∥ !P" shows "!P ==>α ≺ P'" assms (auto simp add: weakTrans_def intro: weakCongRepl)
¤ Dauer der Verarbeitung: 0.1 Sekunden (vorverarbeitet am 2026-11-04) ¤*© Formatika GbR, Deutschland |
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2026-11-01