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Small refactorings for real numbers #1060

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fredrik-bakke opened this issue Mar 7, 2024 · 0 comments
Open
3 tasks

Small refactorings for real numbers #1060

fredrik-bakke opened this issue Mar 7, 2024 · 0 comments
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real-numbers refactoring

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@fredrik-bakke
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Real numbers

  • Factor out lower and upper Dedekind cuts into their own files.
  • lower and upper Dedekind reals should probably be their own files too.
  • Use the theory of lower and upper sets of posets in the definition of Dedekind cuts.
This was referenced Mar 7, 2024
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@malarbol malarbol mentioned this issue Mar 23, 2024
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EgbertRijke added a commit that referenced this issue Apr 11, 2024
@fredrik-bakke @EgbertRijke
Propositional operations (#1008)
11dfe99 
## Summary
- Introduce a general naming scheme for infix endooperations on
propositions and the corresponding endooperations on types
- Remove uses of `∀`
- remove the redundant `implication-Prop`
- Add table for propositional logic
- Add table for operations on propositions
- Correct the definition of exclusive disjunction. It is now named
"exclusive sum" (up for discussion)
- Introduce _disjunction_, (the correct definition of) _exclusive
disjunction_, and _mere logical equivalence_ of types
- Introduce _coinhabitedness_ of types
- Introduce universal quantification
- Define the homotopy preorder of types
- Prove that existential quantification of type families agrees with
existential quantification of the propositional reflection of the type
family
- Prove that disjunction of types agree with disjunction of the
propositional reflections of the summands

Intersects with #1060.
Resolves #984.

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Co-authored-by: Egbert Rijke <[email protected]>
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