Theory: mu

Parents


Type constants


Term constants


Axioms


Definitions

MU
|- !A G. CONTINUOUS G ==> (MU A G = LIM_PROC (\n. ITER n G (STOP A)))

Theorems

EXISTS_MU
|- ?f. !A G. CONTINUOUS G ==> (f A G = LIM_PROC (\n. ITER n G (STOP A)))
IS_PROCESS_MU
|- !A G.
     CHAIN (\n. ITER n G (STOP A)) ==>
     IS_PROCESS (A,IT_UNION (\n. TRACES (ITER n G (STOP A))))
IS_PROCESS_MU'
|- !G A.
     CHAIN (\n. ITER n G (STOP A)) ==>
     CONTINUOUS G ==>
     IS_PROCESS (A,IT_UNION (\n. TRACES (ITER n G (STOP A))))
ALPHA_MU
|- CHAIN (\n. ITER n G (STOP A)) ==> CONTINUOUS G ==> (ALPHA (MU A G) = A)
TRACES_MU
|- CHAIN (\n. ITER n G (STOP A)) ==>
   CONTINUOUS G ==>
   (TRACES (MU A G) = IT_UNION (\n. TRACES (ITER n G (STOP A))))