Hi Jianjun,

> I have difficulty proving something like

> `!x y z. ((x UNION y = z) /\ DISJOINT x y) ==> (x = z DIFF y)`.

> Any help please?

Simple equalities on sets usually fall over if you attack them with
extensionality and METIS_TAC.  In this case, the tactic

   SRW_TAC [][DISJOINT_DEF, EXTENSION] THEN METIS_TAC []

does the job (assuming that you have pred_setTheory open to pick up
the theorems DISJOINT_DEF and EXTENSION).

Michael.

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