Section Multiplication.
Variable (m n p: nat) (x y z: nat).
Hypothesis
(Ex: encodes (sigma (F x)) m) (Ey: encodes (sigma (F y)) n) (Ez: encodes (sigma (F z)) p).

Lemma backward_mult:
sigma • fst (mulEQ x y z) ≡ sigma • snd (mulEQ x y z) -> m * n = p /\ sigma (G x y z) = T n m.