theorem Th22: :: POLYEQ_5:22

for z, a0, a1, a2, s1, s2, a3, s3, s4 being Complex st a3 = - (((s1 + s2) + s3) + s4) & a2 = (((((s1 * s2) + (s1 * s3)) + (s1 * s4)) + (s2 * s3)) + (s2 * s4)) + (s3 * s4) & a1 = - (((((s1 * s2) * s3) + ((s1 * s2) * s4)) + ((s1 * s3) * s4)) + ((s2 * s3) * s4)) & a0 = ((s1 * s2) * s3) * s4 holds
( ((((z |^ 4) + (a3 * (z |^ 3))) + (a2 * (z |^ 2))) + (a1 * z)) + a0 = 0 iff ( z = s1 or z = s2 or z = s3 or z = s4 ) )