DEFINITION ty3_sred_pr0()
TYPE =
∀t1:T.∀t2:T.(pr0 t1 t2)→∀g:G.∀c:C.∀t:T.(ty3 g c t1 t)→(ty3 g c t2 t)
BODY =
assume t1: T
assume t2: T
suppose H: pr0 t1 t2
assume g: G
assume c: C
assume t: T
suppose H0: ty3 g c t1 t
by (wcpr0_refl .)
we proved wcpr0 c c
by (ty3_sred_wcpr0_pr0 . . . . H0 . previous . H)
we proved ty3 g c t2 t
we proved ∀t1:T.∀t2:T.(pr0 t1 t2)→∀g:G.∀c:C.∀t:T.(ty3 g c t1 t)→(ty3 g c t2 t)