for A being Euclidean preIfWhileAlgebra
for X being non empty countable set
for s being Element of Funcs (X,INT)
for T being Subset of (Funcs (X,INT))
for f being Euclidean ExecutionFunction of A, Funcs (X,INT),T
for x, y being Variable of f holds
( (f . (s,(x := y))) . x = s . y & ( for z being Element of X st z <> x holds
(f . (s,(x := y))) . z = s . z ) )