src/Doc/Tutorial/Rules/Force.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Doc/Tutorial/Rules/Force.thy	Tue Aug 28 18:57:32 2012 +0200
@@ -0,0 +1,50 @@
+theory Force imports Main begin 
+  (*Use Divides rather than Main to experiment with the first proof.
+    Otherwise, it is done by the nat_divide_cancel_factor simprocs.*)
+
+declare div_mult_self_is_m [simp del];
+
+lemma div_mult_self_is_m: 
+      "0<n \<Longrightarrow> (m*n) div n = (m::nat)"
+apply (insert mod_div_equality [of "m*n" n])
+apply simp
+done
+
+
+lemma "(\<forall>x. P x) \<and> (\<exists>x. Q x) \<longrightarrow> (\<forall>x. P x \<and> Q x)"
+apply clarify
+oops
+
+text {*
+proof\ {\isacharparenleft}prove{\isacharparenright}{\isacharcolon}\ step\ {\isadigit{1}}\isanewline
+\isanewline
+goal\ {\isacharparenleft}lemma{\isacharparenright}{\isacharcolon}\isanewline
+{\isacharparenleft}{\isasymforall}x{\isachardot}\ P\ x{\isacharparenright}\ {\isasymand}\ {\isacharparenleft}{\isasymexists}x{\isachardot}\ Q\ x{\isacharparenright}\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymforall}x{\isachardot}\ P\ x\ {\isasymand}\ Q\ x{\isacharparenright}\isanewline
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ xa{\isachardot}\ {\isasymlbrakk}{\isasymforall}x{\isachardot}\ P\ x{\isacharsemicolon}\ Q\ xa{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ x\ {\isasymand}\ Q\ x
+*};
+
+text {*
+couldn't find a good example of clarsimp
+
+@{thm[display]"someI"}
+\rulename{someI}
+*};
+
+lemma "\<lbrakk>Q a; P a\<rbrakk> \<Longrightarrow> P (SOME x. P x \<and> Q x) \<and> Q (SOME x. P x \<and> Q x)"
+apply (rule someI)
+oops
+
+lemma "\<lbrakk>Q a; P a\<rbrakk> \<Longrightarrow> P (SOME x. P x \<and> Q x) \<and> Q (SOME x. P x \<and> Q x)"
+apply (fast intro!: someI)
+done
+
+text{*
+proof\ {\isacharparenleft}prove{\isacharparenright}{\isacharcolon}\ step\ \isadigit{1}\isanewline
+\isanewline
+goal\ {\isacharparenleft}lemma{\isacharparenright}{\isacharcolon}\isanewline
+{\isasymlbrakk}Q\ a{\isacharsemicolon}\ P\ a{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}SOME\ x{\isachardot}\ P\ x\ {\isasymand}\ Q\ x{\isacharparenright}\ {\isasymand}\ Q\ {\isacharparenleft}SOME\ x{\isachardot}\ P\ x\ {\isasymand}\ Q\ x{\isacharparenright}\isanewline
+\ \isadigit{1}{\isachardot}\ {\isasymlbrakk}Q\ a{\isacharsemicolon}\ P\ a{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharquery}x\ {\isasymand}\ Q\ {\isacharquery}x
+*}
+
+end
+