for A being preIfWhileAlgebra
for S being non empty set
for T being Subset of S holds
( pr1 (S, the carrier of A) is complying_with_empty-instruction & pr1 (S, the carrier of A) is complying_with_catenation & pr1 (S, the carrier of A) complies_with_if_wrt T & pr1 (S, the carrier of A) complies_with_while_wrt T )