DEFINITION pc3_refl()
TYPE =
∀c:C.∀t:T.(pc3 c t t)
BODY =
assume c: C
assume t: T
(h1)
by (pr3_refl . .)
pr3 c t t
end of h1
(h2)
by (pr3_refl . .)
pr3 c t t
end of h2
by (ex_intro2 . . . . h1 h2)
we proved ex2 T λt0:T.pr3 c t t0 λt0:T.pr3 c t t0
that is equivalent to pc3 c t t
we proved ∀c:C.∀t:T.(pc3 c t t)