Theory: order

Parents


Type constants


Term constants


Axioms


Definitions

PREFIX
|- !s t. s LEQ t = (?u. APPEND s u = t)
IN_TRACE
|- !s t. s In t = (?u v. t = APPEND u (APPEND s v))
MONOTONIC
|- !f. MONOTONIC f = (!s t. s LEQ t ==> f s LEQ f t)

Theorems

LEAST
|- !s. [] LEQ s
REFLEXIVE
|- !s. s LEQ s
ANTI_SYM
|- !s t. s LEQ t /\ t LEQ s ==> (s = t)
TRANS_PREFIX
|- !s t v. s LEQ t /\ t LEQ v ==> s LEQ v
ST_IND_PREFIX
|- !s t x. APPEND [x] s LEQ t = ~(t = []) /\ (x = HD t) /\ s LEQ TL t
ST_IND_PREFIX'
|- !s t x. CONS x s LEQ t = ~(t = []) /\ (x = HD t) /\ s LEQ TL t
TOT_ORDER_PREFIX
|- !s t v. s LEQ v /\ t LEQ v ==> s LEQ t \/ t LEQ s