equal
deleted
inserted
replaced
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 |