(* Note: lemma 1000 *)
lemma llpx_sn_cpx_conf: ∀R. (∀L. reflexive … (R L)) → l_liftable R → l_deliftable_sn R →
- ∀h,g,G,Ls,T1,T2. ⦃G, Ls⦄ ⊢ T1 ➡[h, g] T2 →
- ∀Ld. llpx_sn R 0 T1 Ls Ld → llpx_sn R 0 T2 Ls Ld.
+ ∀h,g,G. s_r_confluent1 … (cpx h g G) (llpx_sn R 0).
#R #H1R #H2R #H3R #h #g #G #Ls #T1 #T2 #H elim H -G -Ls -T1 -T2
[ //
| /3 width=4 by llpx_sn_fwd_length, llpx_sn_sort/