-lemma lsred_inv_appl_dx: ∀p,M,N. M ⇀[p] N → ∀B,A,q. @B.A = M → false::q = p →
- ∃∃C. A ⇀[q] C & @B.C = N.
-#p #M #N * -p -M -N
-[ #B #A #B0 #A0 #p0 #_ #H destruct
-| #p #A #C #_ #B0 #D0 #p0 #H destruct
-| #p #B #D #A #_ #B0 #A0 #p0 #_ #H destruct
-| #p #B #A #C #HAC #B0 #A0 #p0 #H1 #H2 destruct /2 width=3/
-]
-qed-.
-
-lemma lsred_fwd_mult: ∀p,M,N. M ⇀[p] N → #{N} < #{M} * #{M}.