diff options
Diffstat (limited to '')
| -rw-r--r-- | Proj.thy | 12 |
1 files changed, 6 insertions, 6 deletions
@@ -20,7 +20,7 @@ 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 by (derive lem: assms) +unfolding fst_def by (derive lems: 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" @@ -33,14 +33,14 @@ 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)" by (derive lem: assms fst_type) + show "\<And>p. p: \<Sum>x:A. B(x) \<Longrightarrow> B(fst p): U(i)" by (derive lems: 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)" by (wellformed lem: assms(1)) - show "\<And>x. x: A \<Longrightarrow> B(x): U(i)" by (wellformed lem: assms(1)) + show "A: U(i)" by (wellformed lems: assms(1)) + show "\<And>x. x: A \<Longrightarrow> B(x): U(i)" by (wellformed lems: assms(1)) qed fact+ qed fact @@ -51,13 +51,13 @@ proof show "\<And>x y. y: B(x) \<Longrightarrow> y: B(x)" . show "a: A" by fact show "b: B(a)" by fact -qed (simple lem: assms) +qed (simple lems: assms) text "Rule declarations:" lemmas Proj_types [intro] = fst_type snd_type -lemmas Proj_comps [intro] = fst_comp snd_comp +lemmas Proj_comps [comp] = fst_comp snd_comp end
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