# HG changeset patch # User desharna # Date 1683537886 -7200 # Node ID 0f7dc48d8b7fecd46704d9570621add8fa775fe1 # Parent 0f92caebc19a3dd03590b95e94b615e33907fc9c added lemmas count_minus_inter_lt_count_minus_inter_iff and minus_inter_eq_minus_inter_iff diff -r 0f92caebc19a -r 0f7dc48d8b7f NEWS --- a/NEWS Mon May 08 11:16:45 2023 +0200 +++ b/NEWS Mon May 08 11:24:46 2023 +0200 @@ -227,6 +227,8 @@ - Used transp_on and reorder assumptions of lemmas bex_least_element and bex_greatest_element. Minor INCOMPATIBILITIES. - Added lemmas. + count_minus_inter_lt_count_minus_inter_iff + minus_inter_eq_minus_inter_iff mult_mono_strong multeqp_code_iff_reflclp_multp multp_code_iff_multp diff -r 0f92caebc19a -r 0f7dc48d8b7f src/HOL/Library/Multiset.thy --- a/src/HOL/Library/Multiset.thy Mon May 08 11:16:45 2023 +0200 +++ b/src/HOL/Library/Multiset.thy Mon May 08 11:24:46 2023 +0200 @@ -375,6 +375,15 @@ "a \# A + B \ a \# A \ a \# B" by auto +lemma count_minus_inter_lt_count_minus_inter_iff: + "count (M2 - M1) y < count (M1 - M2) y \ y \# M1 - M2" + by (meson count_greater_zero_iff gr_implies_not_zero in_diff_count leI order.strict_trans2 + order_less_asym) + +lemma minus_inter_eq_minus_inter_iff: + "(M1 - M2) = (M2 - M1) \ set_mset (M1 - M2) = set_mset (M2 - M1)" + by (metis add.commute count_diff count_eq_zero_iff diff_add_zero in_diff_countE multiset_eq_iff) + subsubsection \Min and Max\