Commit 37ae9abd by Lawrence Paulson

### trival

parent b41e4757c02f
 ... ... @@ -318,7 +318,7 @@ definition subsubsection \Properties\ text \Here we present some trival properties of {\em mean} and {\em gmean}.\ text \Here we present some trivial properties of {\em mean} and {\em gmean}.\ lemma list_sum_mean: fixes xs::"real list" ... ...
 ... ... @@ -746,7 +746,7 @@ lemma hbexE [elim!]: "\x\<^bold>\A. P x \ (\x. by (unfold HBex_def) blast lemma hball_triv [simp]: "(\x\<^bold>\A. P) = ((\x. x\<^bold>\A) \ P)" \ \Trival rewrite rule.\ \ \trivial rewrite rule.\ by (simp add: HBall_def) lemma hbex_triv [simp]: "(\x\<^bold>\A. P) = ((\x. x\<^bold>\A) \ P)" ... ...
 ... ... @@ -176,7 +176,7 @@ proof - thus ?thesis using assms unfolding cong_def using int_mod_pos_eq large_mod_0 zless_imp_add1_zle by (metis abs_of_nonneg le_less not_less zabs_less_one_iff zmod_trival_iff) by (metis abs_of_nonneg le_less not_less zabs_less_one_iff zmod_trivial_iff) qed (* an intro version of sum_list_0 *) ... ...
 ... ... @@ -936,7 +936,7 @@ Moreover, the coupling relation as well as the invariants become trivial for a i \end{enumerate} Step \ref{sim:sb-sbh} is trivial since the bookkeeping within the additional ghost and history state does not affect the control flow of the transition systems and can be easily removed. Similar the additional @{term \} ghost component can be ignored in Step \ref{sim:delayed-free-flowing}. However, to apply Theorem \ref{thm:simulation} in Step \ref{sim:sbh-delayed} we have to convert from @{term [names_short] "safe_reach_virtual_free_flowing (ts, m, \)"} provided by the preconditions of Theorem \ref{thm:reduction} to the required @{term [names_short] "safe_reach_direct_delayed (ts, m, \)"}. This argument is more involved and we only give a short sketch here. The other direction is trival as every single case for delayed releases (cf. Figure \ref{fig:safe-delayed}) immediately implies the corresponding case for free flowing releases (cf. Figure \ref{fig:safe-virtual-memory}). The other direction is trivial as every single case for delayed releases (cf. Figure \ref{fig:safe-delayed}) immediately implies the corresponding case for free flowing releases (cf. Figure \ref{fig:safe-virtual-memory}). First keep in mind that the predicates ensure that \emph{all} reachable configurations starting from @{term "(ts,m,\)"} are safe, according to the rules for free flowing releases or delayed releases respectively. We show the theorem by contraposition and start with a computation which reaches a configuration @{term c} that is unsafe according to the rules for delayed releases and want to show that there has to be a (potentially other) computation (starting from the same initial state) that leads to an unsafe configuration @{term c'} accroding to free flowing releases. If @{term c} is already unsafe according to free flowing releases we have @{term "c'=c"} and are finished. ... ...
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