equal
deleted
inserted
replaced
747 "K <= M ==> M <= N ==> K <= (N::'a::order multiset)" |
747 "K <= M ==> M <= N ==> K <= (N::'a::order multiset)" |
748 apply (unfold le_multiset_def) |
748 apply (unfold le_multiset_def) |
749 apply (blast intro: mult_less_trans) |
749 apply (blast intro: mult_less_trans) |
750 done |
750 done |
751 |
751 |
752 theorem mult_less_le: "M < N = (M <= N \<and> M \<noteq> (N::'a::order multiset))" |
752 theorem mult_less_le: "(M < N) = (M <= N \<and> M \<noteq> (N::'a::order multiset))" |
753 apply (unfold le_multiset_def) |
753 apply (unfold le_multiset_def) |
754 apply auto |
754 apply auto |
755 done |
755 done |
756 |
756 |
757 text {* Partial order. *} |
757 text {* Partial order. *} |