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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
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