Section G_reduce.
End G_reduce.
Definition Grel m p G :=
lambda lambda (ren (add 2) G) (⟨ enc p A, enc m B⟩ ::: Nil) A B ≡
lambda lambda ⟨ A, B ⟩ ::: (ren (add 2) G) Nil (enc n A) (Succ B).

Lemma multiplication_lambdas M m p:
normal M -> Grel m p M -> (exists M', M = (lambda lambda lambda M') /\ σ p m • M' =  t 0 ::: (τ • M')).