#R #H1R #H2R #H3R #H4R #L1 #L2 #T #H
lapply (s_rs_transitive_lex_inv_isid … H3R) -H3R #H3R
@(rexs_ind_sn … H1R … H) -H -L2
[ /4 width=3 by req_refl, lex_refl, inj, ex2_intro/
| #L0 #L2 #_ #HL02 * #L * #f0 #Hf0 #HL1 #HL0
lapply (req_rex_trans … HL0 … HL02) -L0 // * #f1 #Hf1 #HL2
#R #H1R #H2R #H3R #H4R #L1 #L2 #T #H
lapply (s_rs_transitive_lex_inv_isid … H3R) -H3R #H3R
@(rexs_ind_sn … H1R … H) -H -L2
[ /4 width=3 by req_refl, lex_refl, inj, ex2_intro/
| #L0 #L2 #_ #HL02 * #L * #f0 #Hf0 #HL1 #HL0
lapply (req_rex_trans … HL0 … HL02) -L0 // * #f1 #Hf1 #HL2