src/ZF/upair.ML

     "P(if(Q,x,y)) <-> ((Q --> P(x)) & (~Q --> P(y)))"
  (fn _=> [ (excluded_middle_tac "Q" 1),
            (Asm_simp_tac 1),
            (Asm_simp_tac 1) ]);
 
+(** Rewrite rules for boolean case-splitting: faster than 
+	setloop split_tac[expand_if]
+**)
+
+bind_thm ("expand_if_eq1", read_instantiate [("P", "%x. x = ?b")] expand_if);
+bind_thm ("expand_if_eq2", read_instantiate [("P", "%x. ?a = x")] expand_if);
+
+bind_thm ("expand_if_mem1", read_instantiate [("P", "%x. x : ?b")] expand_if);
+bind_thm ("expand_if_mem2", read_instantiate [("P", "%x. ?a : x")] expand_if);
+
+val expand_ifs = [expand_if_eq1, expand_if_eq2,
+		  expand_if_mem1, expand_if_mem2];
+
+(*Logically equivalent to expand_if_mem2*)
 qed_goal "if_iff" ZF.thy "a: if(P,x,y) <-> P & a:x | ~P & a:y"
  (fn _=> [ (simp_tac (!simpset setloop split_tac [expand_if]) 1) ]);
 
 qed_goal "if_type" ZF.thy
     "[| P ==> a: A;  ~P ==> b: A |] ==> if(P,a,b): A"