1.1 --- a/src/HOL/Conditionally_Complete_Lattices.thy Tue Nov 05 09:45:00 2013 +0100
1.2 +++ b/src/HOL/Conditionally_Complete_Lattices.thy Tue Nov 05 09:45:00 2013 +0100
1.3 @@ -96,6 +96,16 @@
1.4 lemma (in order_bot) bdd_above_bot[simp, intro!]: "bdd_below A"
1.5 by (rule bdd_belowI[of _ bot]) simp
1.6
1.7 +lemma bdd_above_uminus[simp]:
1.8 + fixes X :: "'a::ordered_ab_group_add set"
1.9 + shows "bdd_above (uminus ` X) \<longleftrightarrow> bdd_below X"
1.10 + by (auto simp: bdd_above_def bdd_below_def intro: le_imp_neg_le) (metis le_imp_neg_le minus_minus)
1.11 +
1.12 +lemma bdd_below_uminus[simp]:
1.13 + fixes X :: "'a::ordered_ab_group_add set"
1.14 + shows"bdd_below (uminus ` X) \<longleftrightarrow> bdd_above X"
1.15 + by (auto simp: bdd_above_def bdd_below_def intro: le_imp_neg_le) (metis le_imp_neg_le minus_minus)
1.16 +
1.17 context lattice
1.18 begin
1.19
2.1 --- a/src/HOL/Real.thy Tue Nov 05 09:45:00 2013 +0100
2.2 +++ b/src/HOL/Real.thy Tue Nov 05 09:45:00 2013 +0100
2.3 @@ -919,13 +919,6 @@
2.4 using 1 2 3 by (rule_tac x="Real B" in exI, simp)
2.5 qed
2.6
2.7 -(* TODO: generalize to ordered group *)
2.8 -lemma bdd_above_uminus[simp]: "bdd_above (uminus ` X) \<longleftrightarrow> bdd_below (X::real set)"
2.9 - by (auto simp: bdd_above_def bdd_below_def intro: le_imp_neg_le) (metis le_imp_neg_le minus_minus)
2.10 -
2.11 -lemma bdd_below_uminus[simp]: "bdd_below (uminus ` X) \<longleftrightarrow> bdd_above (X::real set)"
2.12 - by (auto simp: bdd_above_def bdd_below_def intro: le_imp_neg_le) (metis le_imp_neg_le minus_minus)
2.13 -
2.14 instantiation real :: linear_continuum
2.15 begin
2.16