diff options
| -rw-r--r-- | hott/Bool_HoTT.thy | 8 | ||||
| -rw-r--r-- | hott/Propositions.thy | 19 |
2 files changed, 27 insertions, 0 deletions
diff --git a/hott/Bool_HoTT.thy b/hott/Bool_HoTT.thy new file mode 100644 index 0000000..57a57b7 --- /dev/null +++ b/hott/Bool_HoTT.thy @@ -0,0 +1,8 @@ +theory Bool_HoTT +imports + MLTT.Prelude + Propositions + +begin + +end diff --git a/hott/Propositions.thy b/hott/Propositions.thy new file mode 100644 index 0000000..66e34d2 --- /dev/null +++ b/hott/Propositions.thy @@ -0,0 +1,19 @@ +theory Propositions +imports + MLTT.Prelude + Equivalence + +begin + +definition isProp where "isProp A \<equiv> \<Prod>x y: A. x =\<^bsub>A\<^esub> y" +definition isSet where "isSet A \<equiv> \<Prod>x y: A. \<Prod>p q: x =\<^bsub>A\<^esub> y. p =\<^bsub>x =\<^bsub>A\<^esub> y\<^esub> q" + +Theorem isProp_Top: "isProp \<top>" + unfolding isProp_def + by (intros, elims, refl) + +Theorem isProp_Bot: "isProp \<bottom>" + unfolding isProp_def + by (intros, elim) + +end |