src/HOL/Decision_Procs/Dense_Linear_Order.thy
changeset 35043 07dbdf60d5ad
parent 35028 108662d50512
child 35084 e25eedfc15ce
equal deleted inserted replaced
35042:a27b48967b26 35043:07dbdf60d5ad
   635 qed
   635 qed
   636 lemma sum_eq:"((x::'a::ordered_ab_group_add) + t = 0) == (x = - t)"
   636 lemma sum_eq:"((x::'a::ordered_ab_group_add) + t = 0) == (x = - t)"
   637   using eq_diff_eq[where a= x and b=t and c=0] by simp
   637   using eq_diff_eq[where a= x and b=t and c=0] by simp
   638 
   638 
   639 
   639 
   640 interpretation class_dense_linlinordered_field: constr_dense_linorder
   640 interpretation class_dense_linordered_field: constr_dense_linorder
   641  "op <=" "op <"
   641  "op <=" "op <"
   642    "\<lambda> x y. 1/2 * ((x::'a::{linordered_field,number_ring}) + y)"
   642    "\<lambda> x y. 1/2 * ((x::'a::{linordered_field,number_ring}) + y)"
   643 proof (unfold_locales, dlo, dlo, auto)
   643 proof (unfold_locales, dlo, dlo, auto)
   644   fix x y::'a assume lt: "x < y"
   644   fix x y::'a assume lt: "x < y"
   645   from  less_half_sum[OF lt] show "x < (x + y) /2" by simp
   645   from  less_half_sum[OF lt] show "x < (x + y) /2" by simp
   869 fun class_field_ss phi =
   869 fun class_field_ss phi =
   870    HOL_basic_ss addsimps ([@{thm "linorder_not_less"}, @{thm "linorder_not_le"}])
   870    HOL_basic_ss addsimps ([@{thm "linorder_not_less"}, @{thm "linorder_not_le"}])
   871    addsplits [@{thm "abs_split"},@{thm "split_max"}, @{thm "split_min"}]
   871    addsplits [@{thm "abs_split"},@{thm "split_max"}, @{thm "split_min"}]
   872 
   872 
   873 in
   873 in
   874 Ferrante_Rackoff_Data.funs @{thm "class_dense_linlinordered_field.ferrack_axiom"}
   874 Ferrante_Rackoff_Data.funs @{thm "class_dense_linordered_field.ferrack_axiom"}
   875   {isolate_conv = field_isolate_conv, whatis = classfield_whatis, simpset = class_field_ss}
   875   {isolate_conv = field_isolate_conv, whatis = classfield_whatis, simpset = class_field_ss}
   876 end
   876 end
   877 *}
   877 *}
   878 
   878 
   879 lemma upper_bound_finite_set:
   879 lemma upper_bound_finite_set: