for S being non empty set
for T being Subset of S
for A being free ECIW-strict preIfWhileAlgebra
for g being Function of [:S,(ElementaryInstructions A):],S
for F being Function of (Funcs (S,S)),(Funcs (S,S)) st ( for h being Element of Funcs (S,S) holds (F . h) * h = F . h ) holds
ex f being ExecutionFunction of A,S,T st
( f | [:S,(ElementaryInstructions A):] = g & ( for C, I being Element of A
for s being Element of S st not f iteration_terminates_for I \; C,f . (s,C) holds
f . (s,(while (C,I))) = (F . ((curry' f) . (I \; C))) . (f . (s,C)) ) )