equal
deleted
inserted
replaced
1961 |
1961 |
1962 lemma union_left_cancel: "K + M = K + N \<longleftrightarrow> M = (N::'a multiset)" |
1962 lemma union_left_cancel: "K + M = K + N \<longleftrightarrow> M = (N::'a multiset)" |
1963 by (fact add_left_cancel) |
1963 by (fact add_left_cancel) |
1964 |
1964 |
1965 lemma multi_union_self_other_eq: "(A::'a multiset) + X = A + Y \<Longrightarrow> X = Y" |
1965 lemma multi_union_self_other_eq: "(A::'a multiset) + X = A + Y \<Longrightarrow> X = Y" |
1966 by (fact add_imp_eq) |
1966 by (fact add_left_imp_eq) |
1967 |
1967 |
1968 lemma mset_less_trans: "(M::'a multiset) < K \<Longrightarrow> K < N \<Longrightarrow> M < N" |
1968 lemma mset_less_trans: "(M::'a multiset) < K \<Longrightarrow> K < N \<Longrightarrow> M < N" |
1969 by (fact order_less_trans) |
1969 by (fact order_less_trans) |
1970 |
1970 |
1971 lemma multiset_inter_commute: "A #\<inter> B = B #\<inter> A" |
1971 lemma multiset_inter_commute: "A #\<inter> B = B #\<inter> A" |