diff options
| -rw-r--r-- | HoTT_Methods.thy | 4 | ||||
| -rw-r--r-- | Proj.thy | 13 |
2 files changed, 7 insertions, 10 deletions
diff --git a/HoTT_Methods.thy b/HoTT_Methods.thy index 9849195..411176e 100644 --- a/HoTT_Methods.thy +++ b/HoTT_Methods.thy @@ -50,10 +50,10 @@ method derive uses lems = (routine add: lems | compute comp: lems)+ section \<open>Induction\<close> -text " +text \<open> Placeholder section for the automation of induction, i.e. using the elimination rules. At the moment one must directly apply them with \<open>rule X_elim\<close>. -" +\<close> end @@ -7,10 +7,7 @@ Projection functions \<open>fst\<close> and \<open>snd\<close> for the dependent *) theory Proj -imports - HoTT_Methods - Prod - Sum +imports HoTT_Methods Prod Sum begin @@ -28,12 +25,12 @@ unfolding fst_def by compute (derive lems: assms) lemma snd_type: assumes "A: U i" and "B: A \<longrightarrow> U i" and "p: \<Sum>x:A. B x" shows "snd p: B (fst p)" -unfolding snd_def proof - show "\<And>p. p: \<Sum>x:A. B x \<Longrightarrow> B (fst p): U i" by (derive lems: assms fst_type) - +unfolding snd_def proof (derive lems: assms) + show "\<And>p. p: \<Sum>x:A. B x \<Longrightarrow> fst p: A" using assms(1-2) by (rule fst_type) + fix x y assume asm: "x: A" "y: B x" show "y: B (fst <x,y>)" by (derive lems: asm assms fst_comp) -qed fact +qed lemma snd_comp: assumes "A: U i" and "B: A \<longrightarrow> U i" and "a: A" and "b: B a" shows "snd <a,b> \<equiv> b" |