theorem :: AOFA_000:84

for A being preIfWhileAlgebra
for I being Element of A
for S being non empty set
for T being Subset of S
for s being Element of S
for f being ExecutionFunction of A,S,T st s in T holds
( ( f iteration_terminates_for I,s implies f iteration_terminates_for I,f . (s,I) ) & ( f iteration_terminates_for I,f . (s,I) implies f iteration_terminates_for I,s ) & iteration-degree (I,s,f) = 1. + (iteration-degree (I,(f . (s,I)),f)) )