--- a/doc-src/TutorialI/Sets/Functions.thy Tue Aug 28 18:46:15 2012 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,143 +0,0 @@
-theory Functions imports Main begin
-
-
-text{*
-@{thm[display] id_def[no_vars]}
-\rulename{id_def}
-
-@{thm[display] o_def[no_vars]}
-\rulename{o_def}
-
-@{thm[display] o_assoc[no_vars]}
-\rulename{o_assoc}
-*}
-
-text{*
-@{thm[display] fun_upd_apply[no_vars]}
-\rulename{fun_upd_apply}
-
-@{thm[display] fun_upd_upd[no_vars]}
-\rulename{fun_upd_upd}
-*}
-
-
-text{*
-definitions of injective, surjective, bijective
-
-@{thm[display] inj_on_def[no_vars]}
-\rulename{inj_on_def}
-
-@{thm[display] surj_def[no_vars]}
-\rulename{surj_def}
-
-@{thm[display] bij_def[no_vars]}
-\rulename{bij_def}
-*}
-
-
-
-text{*
-possibly interesting theorems about inv
-*}
-
-text{*
-@{thm[display] inv_f_f[no_vars]}
-\rulename{inv_f_f}
-
-@{thm[display] inj_imp_surj_inv[no_vars]}
-\rulename{inj_imp_surj_inv}
-
-@{thm[display] surj_imp_inj_inv[no_vars]}
-\rulename{surj_imp_inj_inv}
-
-@{thm[display] surj_f_inv_f[no_vars]}
-\rulename{surj_f_inv_f}
-
-@{thm[display] bij_imp_bij_inv[no_vars]}
-\rulename{bij_imp_bij_inv}
-
-@{thm[display] inv_inv_eq[no_vars]}
-\rulename{inv_inv_eq}
-
-@{thm[display] o_inv_distrib[no_vars]}
-\rulename{o_inv_distrib}
-*}
-
-text{*
-small sample proof
-
-@{thm[display] ext[no_vars]}
-\rulename{ext}
-
-@{thm[display] fun_eq_iff[no_vars]}
-\rulename{fun_eq_iff}
-*}
-
-lemma "inj f \<Longrightarrow> (f o g = f o h) = (g = h)";
- apply (simp add: fun_eq_iff inj_on_def)
- apply (auto)
- done
-
-text{*
-\begin{isabelle}
-inj\ f\ \isasymLongrightarrow \ (f\ \isasymcirc \ g\ =\ f\ \isasymcirc \ h)\ =\ (g\ =\ h)\isanewline
-\ 1.\ \isasymforall x\ y.\ f\ x\ =\ f\ y\ \isasymlongrightarrow \ x\ =\ y\ \isasymLongrightarrow \isanewline
-\ \ \ \ (\isasymforall x.\ f\ (g\ x)\ =\ f\ (h\ x))\ =\ (\isasymforall x.\ g\ x\ =\ h\ x)
-\end{isabelle}
-*}
-
-
-text{*image, inverse image*}
-
-text{*
-@{thm[display] image_def[no_vars]}
-\rulename{image_def}
-*}
-
-text{*
-@{thm[display] image_Un[no_vars]}
-\rulename{image_Un}
-*}
-
-text{*
-@{thm[display] image_compose[no_vars]}
-\rulename{image_compose}
-
-@{thm[display] image_Int[no_vars]}
-\rulename{image_Int}
-
-@{thm[display] bij_image_Compl_eq[no_vars]}
-\rulename{bij_image_Compl_eq}
-*}
-
-
-text{*
-illustrates Union as well as image
-*}
-
-lemma "f`A \<union> g`A = (\<Union>x\<in>A. {f x, g x})"
-by blast
-
-lemma "f ` {(x,y). P x y} = {f(x,y) | x y. P x y}"
-by blast
-
-text{*actually a macro!*}
-
-lemma "range f = f`UNIV"
-by blast
-
-
-text{*
-inverse image
-*}
-
-text{*
-@{thm[display] vimage_def[no_vars]}
-\rulename{vimage_def}
-
-@{thm[display] vimage_Compl[no_vars]}
-\rulename{vimage_Compl}
-*}
-
-
-end