Take a fresh arbitrary variable . Assuming would provide precisely the witness forbidden by the premise; discharge that assumption before universal introduction.
1. ¬∃x R(x)             premise
2.   R(a)               assumption [i], a fresh
3.   ∃x R(x)            ∃I, 2
4.   ⊥                  ¬E, 1, 3
5. ¬R(a)                ¬I, 2–4, discharging [i]
6. ∀y ¬R(y)             ∀I, 5
At line 6, is free in no undischarged assumption: line 2 has already been discharged. The change of bound variable name is part of the universal-introduction instance.

Ancestors (12)

  1. b
  2. 8
  3. Digital systems, linear algebra, introduction to formal proof
  4. 2018
  5. Past exam of the year 1 of the computer science course of the University of Oxford
  6. Year 1 of the computer science course of the University of Oxford
  7. Computer science course of the University of Oxford
  8. Undergraduate course of the University of Oxford
  9. Course of the University of Oxford
  10. University of Oxford
  11. List of universities
  12. Home

View article source

Discussion (0) New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version