DEFINITION sn3_shift()
TYPE =
∀b:B
.∀c:C.∀v:T.∀t:T.(sn3 c (THead (Bind b) v t))→(sn3 (CHead c (Bind b) v) t)
BODY =
assume b: B
assume c: C
assume v: T
assume t: T
suppose H: sn3 c (THead (Bind b) v t)
(H_x)
by (sn3_gen_bind . . . . H)
land (sn3 c v) (sn3 (CHead c (Bind b) v) t)
end of H_x
(H0) consider H_x
we proceed by induction on H0 to prove sn3 (CHead c (Bind b) v) t
case conj : :sn3 c v H2:sn3 (CHead c (Bind b) v) t ⇒
the thesis becomes the hypothesis H2
we proved sn3 (CHead c (Bind b) v) t
we proved
∀b:B
.∀c:C.∀v:T.∀t:T.(sn3 c (THead (Bind b) v t))→(sn3 (CHead c (Bind b) v) t)