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theory Propositions
imports
MLTT.Prelude
Equivalence
begin
Definition isProp: ":= \<Prod>x y: A. x = y"
where "A: U i" by typechk
Definition isSet: ":=\<Prod>x y: A. \<Prod>p q: x = y. p = q"
where "A: U i" by typechk
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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