A survey of the Theorema project
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
The TH ∃ OREM ∀ project: a progress report
Symbolic computation and automated reasoning
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Mathematical theory exploration
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
The Theorema environment for interactive proof development
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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In this paper, we present a new heuristic proving method for predicate logic, called the PCS method since it proceeds by cycling through various phases of proving (i.e. applying generic inference rules), computing (i.e. simplifying formulae), and solving (i.e. finding witness terms). Although not a complete proving calculus, it does produce very natural proofs for many propositions in elementary analysis like the limit theorems. Thus it appears to be a valuable contribution for many of the routine proofs encountered in exploring mathematical theorems.