- APPEND_ID
-
|- !l l'. (l = APPEND l l') = l' = []
- APPEND_NIL
-
|- !l. APPEND l [] = l
- LENGTH_LESS_EQ
-
|- !l1 l2. LENGTH l1 <= LENGTH l2 ==> (!a. LENGTH l1 < LENGTH (CONS a l2))
- NOT_LENGTH_EQ
-
|- !l2 l1. ~(LENGTH l1 = LENGTH l2) ==> ~(l1 = l2)
- APPEND_EQ_NIL
-
|- !l1 l2. (APPEND l1 l2 = []) = (l1 = []) /\ (l2 = [])
- NULL_EQ_NIL
-
|- !l. (l = []) = NULL l
- HD_APPEND
-
|- !l. ~(l = []) ==> (!l'. HD (APPEND l l') = HD l)
- TL_APPEND
-
|- !l. ~(l = []) ==> (!l'. TL (APPEND l l') = APPEND (TL l) l')
- ONE_MEMBER_LIST
-
|- !s t a. (APPEND s t = [a]) ==> (s = []) \/ (s = [a])
- CONS_MEMBER_LIST
-
|- !s s' t a.
(APPEND s t = CONS a s') ==>
(s = []) \/ (?r. (s = CONS a r) /\ (s' = APPEND r t))
- CONS_EQ_APPEND
-
|- !a l. CONS a l = APPEND [a] l