Proof by analogy in mural

One of the most important advantages of using a formal method of developing software is that one can prove that development steps are correct with respect to their specification. Conducting proofs by hand, however,can be time consuming to the extent that designers have to judge whether a proof of a particular obligation is worth conducting. Even if hand proofs are worth conducting, how do we know that they are correct? One approach to overcoming this problem is to use an automatic theorem proving system to develop and check our proofs. However, in order to enable present day theorem provers to check proofs, one has to conduct them in much more detail than hand proofs. Carrying out more detailed proofs is of course more time consuming. This paper describes the use of proof by analogy in an attempt to reduce the time spent on proofs. We develop and implement a proof follower based on analogy and present two examples to illustrate its characteristics. One example illustrates the successful use of the proof follower. The other example illustrates that the follower's failure can provide a hint that enables the user to complete a proof

A comparison of colour Doppler sonography and the pelvic arteriogram in assessment of patients with gestational trophoblastic disease

Objective To assess whether colour Doppler sonography can replace pelvic arteriography in the assessment of patients with gestational trophoblastic disease. Design An observational study in which patients with gestational trophoblastic disease were assessed with both pelvic arteriography and colour Doppler sonography. Setting The oncology unit of the Department of Obstetrics and Gynaecology, University of Hong Kong. The unit is the main tertiary referral centre for treatment of trophoblastic diseases in Hong Kong. Subjects Thirty‐two consecutive women referred over an 18 month period. Main outcome measures The site of localisation of the tumour and the size of the tumour as assessed by both methods. Results Eleven patients had a spontaneous fall of β‐hCGtitres and did not have pelvic arteriograms performed. The remaining 21 patients had both investigations performed. Four patients had no evidence of abnormal pelvic vessels either on colour Doppler sonography or on pelvic arteriography. Their raised P hCG titres were due to metastatic disease elsewhere. In the remaining patients the location of the tumour vessels was found to be concordant between the two methods of imaging. Measurements of the mean diameter of tumour bulk by the two methods also agreed well (r = 0.93, P < 0–0001). Pelvic arteriogram over‐estimated the size of the tumour in two patients by 2 and 3 cm, respectively, but this did not alter the risk categories of the patients. Conclusion Colour Doppler sonography is a noninvasive technique that can replace pelvic arteriography in the assessment of patients with trophoblastic diseases