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authorJosh Chen2018-08-30 00:51:48 +0200
committerJosh Chen2018-08-30 00:51:48 +0200
commit2a2e8e46e0de6f99154a9421f75ae802557f22c7 (patch)
tree8dfcd36ddc5ea1da6609dbc06c2a273e36e1a1b6 /ex/HoTT book
parenta7b46d4b0204571ba9124accebc84f77ae0bed26 (diff)
Should write the correct rule for Ord_leq_min. Another exercise.
Diffstat (limited to 'ex/HoTT book')
-rw-r--r--ex/HoTT book/Ch1.thy12
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