-lemma lprs_step_dx (h) (G): ∀L1,L. ⦃G, L1⦄ ⊢ ➡*[h] L →
- ∀L2. ⦃G, L⦄ ⊢ ➡[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
-/3 width=3 by lpr_cprs_trans, lex_CTC_step_dx/ qed-.
+lemma lprs_step_dx (h) (G):
+ ∀L1,L. ❪G,L1❫ ⊢ ➡*[h,0] L →
+ ∀L2. ❪G,L❫ ⊢ ➡[h,0] L2 → ❪G,L1❫ ⊢ ➡*[h,0] L2.
+/4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_dx/ qed-.
+
+lemma lprs_strip (h) (G):
+ confluent2 … (lprs h 0 G) (lpr h 0 G).
+#h #G #L0 #L1 #HL01 #L2 #HL02
+elim (TC_strip1 … L1 ?? HL02) -HL02
+[ /3 width=3 by lprs_TC, ex2_intro/ | skip
+| /2 width=1 by lprs_inv_TC/
+| /2 width=3 by lpr_conf/
+]
+qed-.