DEFINITION nf2_appl_lref()
TYPE =
∀c:C
.∀u:T
.nf2 c u
→∀i:nat.(nf2 c (TLRef i))→(nf2 c (THead (Flat Appl) u (TLRef i)))
BODY =
assume c: C
assume u: T
suppose H: nf2 c u
assume i: nat
suppose H0: nf2 c (TLRef i)
(H_y)
by (nf2_appls_lref . . H0 .)
nfs2 c (TCons u TNil)
→nf2 c (THeads (Flat Appl) (TCons u TNil) (TLRef i))
end of H_y
by (conj . . H I)
we proved land (nf2 c u) True
that is equivalent to nfs2 c (TCons u TNil)
by (H_y previous)
we proved nf2 c (THeads (Flat Appl) (TCons u TNil) (TLRef i))
that is equivalent to nf2 c (THead (Flat Appl) u (TLRef i))
we proved
∀c:C
.∀u:T
.nf2 c u
→∀i:nat.(nf2 c (TLRef i))→(nf2 c (THead (Flat Appl) u (TLRef i)))