diff options
Diffstat (limited to '')
| -rw-r--r-- | Proj.thy | 32 |
1 files changed, 12 insertions, 20 deletions
@@ -21,17 +21,14 @@ text "Typing judgments and computation rules for the dependent and non-dependent lemma fst_type: assumes "\<Sum>x:A. B(x): U(i)" and "p: \<Sum>x:A. B(x)" shows "fst(p): A" -unfolding fst_def -proof - show "A: U(i)" using assms(1) by (rule Sum_wellform) -qed (fact assms | assumption)+ +unfolding fst_def by (derive lem: assms) lemma fst_comp: assumes "A: U(i)" and "B: A \<longrightarrow> U(i)" and "a: A" and "b: B(a)" shows "fst(<a,b>) \<equiv> a" unfolding fst_def proof - show "\<And>x. x: A \<Longrightarrow> x: A" . + show "a: A" and "b: B(a)" by fact+ qed (rule assms)+ @@ -39,20 +36,16 @@ lemma snd_type: assumes "\<Sum>x:A. B(x): 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)" - proof - - have "\<And>p. p: \<Sum>x:A. B(x) \<Longrightarrow> fst(p): A" using assms(1) by (rule fst_type) - with assms(1) show "\<And>p. p: \<Sum>x:A. B(x) \<Longrightarrow> B(fst p): U(i)" by (rule Sum_wellform) - qed - + show "\<And>p. p: \<Sum>x:A. B(x) \<Longrightarrow> B(fst p): U(i)" by (derive lem: assms fst_type) + fix x y assume asm: "x: A" "y: B(x)" show "y: B(fst <x,y>)" proof (subst fst_comp) - show "A: U(i)" using assms(1) by (rule Sum_wellform) - show "\<And>x. x: A \<Longrightarrow> B(x): U(i)" using assms(1) by (rule Sum_wellform) - qed (rule asm)+ -qed (fact assms) + show "A: U(i)" by (wellformed lem: assms(1)) + show "\<And>x. x: A \<Longrightarrow> B(x): U(i)" by (wellformed lem: assms(1)) + qed fact+ +qed fact lemma snd_comp: @@ -60,13 +53,12 @@ lemma snd_comp: unfolding snd_def proof show "\<And>x y. y: B(x) \<Longrightarrow> y: B(x)" . - show "a: A" by (fact assms) - show "b: B(a)" by (fact assms) - show *: "B(a): U(i)" using assms(3) by (rule assms(2)) - show "B(a): U(i)" by (fact *) -qed + show "a: A" by fact + show "b: B(a)" by fact +qed (simple lem: assms) +lemmas Proj_types [intro] = fst_type snd_type lemmas Proj_comps [intro] = fst_comp snd_comp |