Theory: list_lib1

Parents


Type constants


Term constants


Axioms


Definitions


Theorems

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