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By Maurice Holt
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For uy = t: We need to show (uρϕ )y = tρϕ . But (uρϕ )y = ((λyt)ϕ )y = tϕ = tρϕ since u does not appear in t. For (r = s) ∈ C: We need to show (r = s)ϕ. But this clearly follows from (r = s)ρϕ . 2. Deﬁnition of Φ : U-solutions → U -solutions, and proof of Φ (Φϕ) = ϕ. For a U-solution ϕ deﬁne Φϕ = ϕ Q∃ . Then uρϕ = λytϕ = λytϕ = uϕ, and clearly vρϕ = vϕ for all other ﬂexible ϕ. For (r = s) ∈ C, from rϕ = sϕ we easily obtain rϕ = sϕ . It is not hard to see that the uniﬁcation algorithm terminates, by deﬁning a measure that decreases with each transition.
Proof planning is a technique for guiding the search for a proof in automated theorem proving. A proof plan is an outline or plan of a proof. To prove a conjecture, proof planning constructs a proof plan for a proof and uses it to guide the construction of the proof itself. Proof planning reduces the amount of search and curbs the combinatorial explosion. It also helps pinpoint the cause of any proof attempt failure, suggesting a patch to facilitate a renewed attempt. The research reported in this paper was supported by EPSRC grant GR/S01771.
1992). The Use of Planning Critics in Mechanizing Inductive Proofs. ), International Conference on Logic Programming and Automated Reasoning – LPAR 92, St. Petersburg, Lecture Notes in Artiﬁcial Intelligence No. 624, pages 178–189. Springer-Verlag. Also available from Edinburgh as DAI Research Paper 592. [Jackson & Lowe, 2000] Jackson, M. and Lowe, H. (June 2000). XBarnacle: Making theorem provers more accessible. ), CADE17, number 1831 in Lecture Notes in Computer Science, Pittsburg. Springer.
2nd Int'l Conference on Numerical Methods in Fluid Dynamics by Maurice Holt