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Combining Higher-Order Logic with Set Theory Formalizations.

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This summary is machine-generated.

This study connects Isabelle/HOL and Isabelle/Mizar libraries by defining isomorphisms for core concepts like real numbers. This enables simultaneous theorem use and knowledge transfer between these foundational systems.

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Area of Science:

  • Formal methods
  • Mathematical logic
  • Computer science

Background:

  • Isabelle/HOL and Isabelle/Mizar offer distinct foundational libraries.
  • These libraries independently define basic concepts, leading to disconnected results.
  • A unified approach is needed to leverage both formal systems.

Purpose of the Study:

  • To align significant parts of the Isabelle/HOL and Isabelle/Mizar libraries.
  • To establish isomorphisms between their independently defined concepts.
  • To enable simultaneous use and transport of theorems between the two foundational systems.

Main Methods:

  • Defining isomorphisms between key concepts in Isabelle/HOL and Isabelle/Mizar.
  • Focusing on foundational elements such as real numbers and algebraic structures.
  • Utilizing formal verification techniques within the Isabelle framework.

Main Results:

  • Successful alignment of significant portions of the two libraries.
  • Establishment of isomorphisms for concepts including real numbers and algebraic structures.
  • Demonstration of theorem transportability between the foundations.

Conclusions:

  • The defined isomorphisms bridge the gap between Isabelle/HOL and Isabelle/Mizar.
  • This alignment allows for simultaneous utilization of results from both libraries.
  • Enables enhanced knowledge sharing and theorem proving capabilities.