#RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
/4 width=5 by lexs_refl, lexs_next, step, inj/
qed.
lemma lexs_tc_push_sn: ∀RN,RP. c_reflexive … RP →
∀f,I2,L1,L2. TC … (lexs RN RP f) L1 L2 → ∀I1. RP L1 I1 I2 →
#RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
/4 width=5 by lexs_refl, lexs_next, step, inj/
qed.
lemma lexs_tc_push_sn: ∀RN,RP. c_reflexive … RP →
∀f,I2,L1,L2. TC … (lexs RN RP f) L1 L2 → ∀I1. RP L1 I1 I2 →