theorem Th53: :: AOFA_000:53

for A being preIfWhileAlgebra
for I being Element of A holds
( not I nin ElementaryInstructions A or I = EmptyIns A or ex I1, I2 being Element of A st
( I = I1 \; I2 & I1 <> I1 \; I2 & I2 <> I1 \; I2 ) or ex C, I1, I2 being Element of A st I = if-then-else (C,I1,I2) or ex C, J being Element of A st I = while (C,J) )