-[ #B #A #B0 #A0 #p0 #_ #H destruct
-| #p #A #C #_ #B0 #D0 #p0 #H destruct
-| #p #B #D #A #HBD #B0 #A0 #p0 #H1 #H2 destruct /2 width=3/
-| #p #B #A #C #_ #B0 #A0 #p0 #_ #H destruct
-]
-qed-.
-
-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/
+[ #B #A #q #H destruct
+| #p #A1 #A2 #_ #q #H destruct
+| #p #B1 #B2 #A #_ #q #H destruct
+| #p #B #A1 #A2 #HA12 #q #H destruct /2 width=6/