# [isabelle] Simplifying addition and subtraction of multisets

```Hallo,

```
I have terms like "{#a,b,c,d#} - {#b#}", which desugars to "(single a + single b + single c + single d) - single b". This is obviously equal to "{#a,c,d#}".
```
```
However, the simplifier fails to prove this and I was not able to find a setup of existing simplification rules to solve it.
```
I ended up proving the following rule, which works in my particular case:

lemma multiset_Diff_single_normalize:
fixes a c assumes "a â c"
shows   "({#a#} + B) - {#c#} = {#a#} + (B - {#c#})"

```
This, combined with add_ac, does the trick. (but only because I can, in this particular instance, decide whether two elements are equal, i.e. I know that b != c and b != d, even though the simplification of "{#a,b,c,d#} - {#b#}" would be sound even if that were not the case)
```

Is there some existing simproc that can be set up to do this automatically?

Cheers,

Manuel

```

This archive was generated by a fusion of Pipermail (Mailman edition) and MHonArc.