Inhabited types. Let $)-\text{'}$ a type We say that $$ is inhabited if there exists MinAt

such that $M$:$.$ For an environment $,$ we say that $$ is $-$inhabited if there exists $M$ in

Atsuch that $|--M$:$.$

Exercise $7.$ Note that the set $T^{-}$syntactically coincides with a certain fragment of the

formulas of Intuitionistic Propositional Logic. Prove that if a type $)-$is inhabited,

then

$,$ when understood as a formula of Intuitionistic Propositional Logic, is valid.$/$