[isabelle] incompatible operand type



Hi 
 
when design a new unknown function max, it return incompatible operand type error, I tried add bracket, still got error, where is wrong?
 
lemma max_app [simp]: "((max xs) @ (max ys)) @ (max zs) = (max xs) @ ((max ys) @ (max zs))"
 
Type unification failed: Clash of types "_ ⇒ _" and "_ list"
Type error in application: incompatible operand type
Operator:  op @ :: ??'a list ⇒ ??'a list ⇒ ??'a list
Operand:   max xs :: ??'b ⇒ ??'b
 
lemma max_app [simp]: "(max xs @ max ys) @ max zs = max xs @ (max ys @ max zs)"
apply(induct_tac xs)
apply(auto)
done
 
Regards,
 
Martin
 		 	   		  


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