Theory: restrict

Parents


Type constants


Term constants


Axioms


Definitions

RESTRICT
|- (!A. RESTRICT [] A = []) /\
   (!x t A.
     RESTRICT (CONS x t) A =
     ((x IN A) => (CONS x (RESTRICT t A)) | (RESTRICT t A)))

Theorems

STRICT_REST
|- !A. RESTRICT [] A = []
DISTRIB_REST
|- !s t A. RESTRICT (APPEND s t) A = APPEND (RESTRICT s A) (RESTRICT t A)
RESTR_EMPTY
|- !s. RESTRICT s {} = []
REP_RESTR
|- !s A B. RESTRICT (RESTRICT s A) B = RESTRICT s (A INTER B)
MAX_LEN_REST
|- !A s. LENGTH (RESTRICT s A) <= LENGTH s
REST_LEMMA
|- !A s a. ~(LENGTH (RESTRICT s A) = LENGTH (CONS a s))
REST_CONS_THM
|- !a A s. ~(RESTRICT s A = CONS a s)