Dafny multisets

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In a reference manual (http://www.cse.unsw.edu.au/~se2011/DafnyDocumentation/Dafny%20-%20ValueTypes.pdf), we can find: two multisets are equal if they have exactly the same count of each element. However, there is no violation if I assert:

   assert multiset({1,1}) == multiset{1};

So I am understanding something wrong.

Then, for instance, to prove this:

lemma seqSplit(s:seq<int>, c:int, p:int, f:int)
       requires 0<=c<=p<=f+1<=|s|
       ensures multiset(s[c..f+1]) == multiset(s[c..p])+multiset(s[p..f+1])

What is is necessary? I started with:

       assert forall i :: c<=i<=f ==> 
              (s[i] in multiset(s[c..f+1]) <==> (s[i] in multiset(s[c..p]) || s[i] in multiset(s[p..f+1])));

It verifies, and I would say it is the same as in the ensures, but seems not. Any help?

theorem-proving dafny multiset
1 Answers

multiset({1,1}) means "construct the set {1,1}, and then convert it to a multiset". Since the set {1,1} and the set {1} are the same, your assertion passes.

I think you want multiset{1,1}.

user_4382670
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