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theory Propositions
imports
MLTT.Prelude
Equivalence
begin
definition isProp where "isProp A ≡ ∏x y: A. x =⇘A⇙ y"
definition isSet where "isSet A ≡ ∏x y: A. ∏p q: x =⇘A⇙ y. p =⇘x =⇘A⇙ y⇙ q"
Theorem isProp_Top: "isProp ⊤"
unfolding isProp_def
by (intros, elims, refl)
Theorem isProp_Bot: "isProp ⊥"
unfolding isProp_def
by (intros, elim)
end
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