The complexity of linear problems in fields
Journal of Symbolic Computation
The complexity of almost linear diophantine problems
Journal of Symbolic Computation
The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
Mixed real-integer linear quantifier elimination
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Autarkic Computations in Formal Proofs
Journal of Automated Reasoning
Programming and Computing in HOL
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
An Automata-Theoretic Approach to Presburger Arithmetic Constraints (Extended Abstract)
SAS '95 Proceedings of the Second International Symposium on Static Analysis
Computational Metatheory in Nuprl
Proceedings of the 9th International Conference on Automated Deduction
Elementary bounds for presburger arithmetic
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Presburger arithmetic with bounded quantifier alternation
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Dependent types ensure partial correctness of theorem provers
Journal of Functional Programming
On the Automata Size for Presburger Arithmetic
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
An effective decision procedure for linear arithmetic over the integers and reals
ACM Transactions on Computational Logic (TOCL)
An online proof-producing decision procedure for mixed-integer linear arithmetic
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Verifying and reflecting quantifier elimination for presburger arithmetic
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
An interpretation of Isabelle/HOL in HOL light
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Importing HOL into Isabelle/HOL
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
A proof-producing decision procedure for real arithmetic
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Proof Synthesis and Reflection for Linear Arithmetic
Journal of Automated Reasoning
Pattern minimization problems over recursive data types
Proceedings of the 13th ACM SIGPLAN international conference on Functional programming
Context Aware Calculation and Deduction
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Parametric Linear Arithmetic over Ordered Fields in Isabelle/HOL
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Don't care words with an application to the automata-based approach for real addition
Formal Methods in System Design
Journal of Automated Reasoning
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We present a formally verified quantifier elimination procedure for the first order theory over linear mixed real-integer arithmetics in higher-order logic based on a work by Weispfenning. To this end we provide two verified quantifier elimination procedures: for Presburger arithmitics and for linear real arithmetics.