DEFINITION iso_refl()
TYPE =
∀t:T.(iso t t)
BODY =
assume t: T
we proceed by induction on t to prove iso t t
case TSort : n:nat ⇒
the thesis becomes iso (TSort n) (TSort n)
by (iso_sort . .)
iso (TSort n) (TSort n)
case TLRef : n:nat ⇒
the thesis becomes iso (TLRef n) (TLRef n)
by (iso_lref . .)
iso (TLRef n) (TLRef n)
case THead : k:K t0:T t1:T ⇒
the thesis becomes iso (THead k t0 t1) (THead k t0 t1)
() by induction hypothesis we know iso t0 t0
() by induction hypothesis we know iso t1 t1
by (iso_head . . . . .)
iso (THead k t0 t1) (THead k t0 t1)
we proved iso t t
we proved ∀t:T.(iso t t)