DEFINITION subst1_gen_sort()
TYPE =
∀v:T.∀x:T.∀i:nat.∀n:nat.(subst1 i v (TSort n) x)→(eq T x (TSort n))
BODY =
assume v: T
assume x: T
assume i: nat
assume n: nat
suppose H: subst1 i v (TSort n) x
we proceed by induction on H to prove eq T x (TSort n)
case subst1_refl : ⇒
the thesis becomes eq T (TSort n) (TSort n)
by (refl_equal . .)
eq T (TSort n) (TSort n)
case subst1_single : t2:T H0:subst0 i v (TSort n) t2 ⇒
the thesis becomes eq T t2 (TSort n)
by (subst0_gen_sort . . . . H0 .)
eq T t2 (TSort n)
we proved eq T x (TSort n)
we proved ∀v:T.∀x:T.∀i:nat.∀n:nat.(subst1 i v (TSort n) x)→(eq T x (TSort n))