diff options
| -rw-r--r-- | ProdProps.thy | 1 | ||||
| -rw-r--r-- | ex/HoTT book/Ch1.thy | 2 | ||||
| -rw-r--r-- | ex/Synthesis.thy | 2 |
3 files changed, 2 insertions, 3 deletions
diff --git a/ProdProps.thy b/ProdProps.thy index 7071b39..adadb29 100644 --- a/ProdProps.thy +++ b/ProdProps.thy @@ -21,7 +21,6 @@ text " lemma compose_assoc: assumes "A: U(i)" and "f: A \<rightarrow> B" "g: B \<rightarrow> C" "h: \<Prod>x:C. D(x)" shows "(h \<circ> g) \<circ> f \<equiv> h \<circ> (g \<circ> f)" - proof (subst (0 1 2 3) compose_def) show "\<^bold>\<lambda>x. (\<^bold>\<lambda>y. h`(g`y))`(f`x) \<equiv> \<^bold>\<lambda>x. h`((\<^bold>\<lambda>y. g`(f`y))`x)" proof (subst Prod_eq) diff --git a/ex/HoTT book/Ch1.thy b/ex/HoTT book/Ch1.thy index 65de875..cc0adf5 100644 --- a/ex/HoTT book/Ch1.thy +++ b/ex/HoTT book/Ch1.thy @@ -13,7 +13,7 @@ chapter \<open>HoTT Book, Chapter 1\<close> section \<open>1.6 Dependent pair types (\<Sigma>-types)\<close> -text "Prove that the only inhabitants of the \<Sigma>-type are those given by the pair constructor." +text "Propositional uniqueness principle:" schematic_goal assumes "(\<Sum>x:A. B(x)): U(i)" and "p: \<Sum>x:A. B(x)" diff --git a/ex/Synthesis.thy b/ex/Synthesis.thy index cd5c4e1..e5a8ecf 100644 --- a/ex/Synthesis.thy +++ b/ex/Synthesis.thy @@ -76,4 +76,4 @@ theorem by (simple lems: pred_welltyped pred_type pred_props) -end
\ No newline at end of file +end |