theorem Th5: :: AMI_4:5

for s being State of SCM
for P being Instruction-Sequence of SCM st Euclid-Algorithm c= P holds
for k being Nat st IC (Comput (P,s,k)) = 3 holds
( ( (Comput (P,s,k)) . (dl. 1) > 0 implies IC (Comput (P,s,(k + 1))) = 0 ) & ( (Comput (P,s,k)) . (dl. 1) <= 0 implies IC (Comput (P,s,(k + 1))) = 4 ) & (Comput (P,s,(k + 1))) . (dl. 0) = (Comput (P,s,k)) . (dl. 0) & (Comput (P,s,(k + 1))) . (dl. 1) = (Comput (P,s,k)) . (dl. 1) )