DEFINITION nf2_sort()
TYPE =
∀c:C.∀n:nat.(nf2 c (TSort n))
BODY =
assume c: C
assume n: nat
we must prove nf2 c (TSort n)
or equivalently ∀t2:T.(pr2 c (TSort n) t2)→(eq T (TSort n) t2)
assume t2: T
suppose H: pr2 c (TSort n) t2
(h1)
by (refl_equal . .)
eq T (TSort n) (TSort n)
end of h1
(h2)
by (pr2_gen_sort . . . H)
eq T t2 (TSort n)
end of h2
by (eq_ind_r . . . h1 . h2)
we proved eq T (TSort n) t2
we proved ∀t2:T.(pr2 c (TSort n) t2)→(eq T (TSort n) t2)
that is equivalent to nf2 c (TSort n)
we proved ∀c:C.∀n:nat.(nf2 c (TSort n))