Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Automated geometry theorem proving by vector calculation
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
On the Mechanization of Real Analysis in Isabelle/HOL
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
Clifford Algebraic Calculus for Geometric Reasoning with Application to Computer Vision
Selected Papers from the International Workshop on Automated Deduction in Geometry
Proving Newton's Propositio Kepleriana Using Geometry and Nonstandard Analysis in Isabelle
ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
The Use of Explicit Plans to Guide Inductive Proofs
Proceedings of the 9th International Conference on Automated Deduction
Lemma Discovery in Automated Induction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Proving Geometric Theorems Using Clifford Algebra and Rewrite Rules
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
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This paper describes ongoing work in our formal investigation of some of the concepts and properties that arise when infinitesimal notions are introduced in a geometry theory. An algebraic geometry theory is developed in the theorem prover Isabelle using hyperreal vectors. We follow a strictly definitional approach and build our theory of vectors within the nonstandard analysis (NSA) framework developed in Isabelle. We show how this theory can be used to give intuitive, yet rigorous, nonstandard proofs of standard geometric theorems through the use of infinitesimal and infinite geometric quantities.