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Diffstat (limited to '')
| -rw-r--r-- | ex/HoTT book/Ch1.thy | 12 |
1 files changed, 12 insertions, 0 deletions
diff --git a/ex/HoTT book/Ch1.thy b/ex/HoTT book/Ch1.thy index d5f05dd..a577fca 100644 --- a/ex/HoTT book/Ch1.thy +++ b/ex/HoTT book/Ch1.thy @@ -40,4 +40,16 @@ proof (rule Sum_elim[where ?p=p]) qed (derive lems: assms) +section \<open>Exercises\<close> + +text "Exercise 1.13" + +abbreviation "not" ("\<not>'(_')") where "\<not>(A) \<equiv> A \<rightarrow> \<zero>" + +text "This proof requires the use of universe cumulativity." + +proposition assumes "A: U(i)" shows "\<^bold>\<lambda>f. f`(inr(\<^bold>\<lambda>a. f`inl(a))): \<not>(\<not>(A + \<not>(A)))" +by (derive lems: assms U_cumulative[where ?A=\<zero> and ?i=O and ?j=i]) + + end |