src/HOL/Lattices.thy
changeset 46882 6242b4bc05bc
parent 46691 72d81e789106
child 46884 154dc6ec0041
equal deleted inserted replaced
46872:bad72cba8a92 46882:6242b4bc05bc
   648 begin
   648 begin
   649 
   649 
   650 definition
   650 definition
   651   "f \<sqinter> g = (\<lambda>x. f x \<sqinter> g x)"
   651   "f \<sqinter> g = (\<lambda>x. f x \<sqinter> g x)"
   652 
   652 
   653 lemma inf_apply (* CANDIDATE [simp, code] *):
   653 lemma inf_apply [simp] (* CANDIDATE [code] *):
   654   "(f \<sqinter> g) x = f x \<sqinter> g x"
   654   "(f \<sqinter> g) x = f x \<sqinter> g x"
   655   by (simp add: inf_fun_def)
   655   by (simp add: inf_fun_def)
   656 
   656 
   657 definition
   657 definition
   658   "f \<squnion> g = (\<lambda>x. f x \<squnion> g x)"
   658   "f \<squnion> g = (\<lambda>x. f x \<squnion> g x)"
   659 
   659 
   660 lemma sup_apply (* CANDIDATE [simp, code] *):
   660 lemma sup_apply [simp] (* CANDIDATE [code] *):
   661   "(f \<squnion> g) x = f x \<squnion> g x"
   661   "(f \<squnion> g) x = f x \<squnion> g x"
   662   by (simp add: sup_fun_def)
   662   by (simp add: sup_fun_def)
   663 
   663 
   664 instance proof
   664 instance proof
   665 qed (simp_all add: le_fun_def inf_apply sup_apply)
   665 qed (simp_all add: le_fun_def inf_apply sup_apply)
   675 begin
   675 begin
   676 
   676 
   677 definition
   677 definition
   678   fun_Compl_def: "- A = (\<lambda>x. - A x)"
   678   fun_Compl_def: "- A = (\<lambda>x. - A x)"
   679 
   679 
   680 lemma uminus_apply (* CANDIDATE [simp, code] *):
   680 lemma uminus_apply [simp] (* CANDIDATE [code] *):
   681   "(- A) x = - (A x)"
   681   "(- A) x = - (A x)"
   682   by (simp add: fun_Compl_def)
   682   by (simp add: fun_Compl_def)
   683 
   683 
   684 instance ..
   684 instance ..
   685 
   685 
   689 begin
   689 begin
   690 
   690 
   691 definition
   691 definition
   692   fun_diff_def: "A - B = (\<lambda>x. A x - B x)"
   692   fun_diff_def: "A - B = (\<lambda>x. A x - B x)"
   693 
   693 
   694 lemma minus_apply (* CANDIDATE [simp, code] *):
   694 lemma minus_apply [simp] (* CANDIDATE [code] *):
   695   "(A - B) x = A x - B x"
   695   "(A - B) x = A x - B x"
   696   by (simp add: fun_diff_def)
   696   by (simp add: fun_diff_def)
   697 
   697 
   698 instance ..
   698 instance ..
   699 
   699