src/HOL/Decision_Procs/Dense_Linear_Order.thy
changeset 30729 461ee3e49ad3
parent 30652 752329615264
child 30741 9e23e3ea7edd
equal deleted inserted replaced
30728:f0aeca99b5d9 30729:461ee3e49ad3
   635 qed
   635 qed
   636 lemma sum_eq:"((x::'a::pordered_ab_group_add) + t = 0) == (x = - t)"
   636 lemma sum_eq:"((x::'a::pordered_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_ordered_field_dense_linear_order!: constr_dense_linear_order
   640 interpretation class_ordered_field_dense_linear_order: constr_dense_linear_order
   641  "op <=" "op <"
   641  "op <=" "op <"
   642    "\<lambda> x y. 1/2 * ((x::'a::{ordered_field,recpower,number_ring}) + y)"
   642    "\<lambda> x y. 1/2 * ((x::'a::{ordered_field,recpower,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