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Here is an introduction paper on theorem-prover based formal method:
G. Chen</SPAN> and F. Liu, </SPAN>Proofs of correctness and properties of integer adder circuits, </SPAN> </SPAN> in IEEE Transactions on Computers, Vol. 59, No. 1, Jan., 2010.</SPAN></SPAN>
Automatic (i.e. non theorem-proving based) techniques can verify adders, comparators, etc. even if they are huge. Most commercial and free tools do that.
Multipliers and dividers are more tricky. Some techniques such as using *BMDs (Binary Moment Diagrams) have been popular some 15 years ago for that.