qed.
lemma tc_lfxs_lex_lfeq: ∀R. c_reflexive … R →
- â\88\80L1,L. L1 ⪤[LTC â\80¦ R] L â\86\92 â\88\80L2,T. L â\89¡[T] L2 →
+ â\88\80L1,L. L1 ⪤[LTC â\80¦ R] L â\86\92 â\88\80L2,T. L â\89\90[T] L2 →
L1 ⪤**[R, T] L2.
/3 width=3 by tc_lfxs_lex, tc_lfxs_step_dx, lfeq_fwd_lfxs/ qed.
s_rs_transitive … R (λ_.lex R) →
lfeq_transitive R →
∀L1,L2,T. L1 ⪤**[R, T] L2 →
- â\88\83â\88\83L. L1 ⪤[LTC â\80¦ R] L & L â\89¡[T] L2.
+ â\88\83â\88\83L. L1 ⪤[LTC â\80¦ R] L & L â\89\90[T] L2.
#R #H1R #H2R #H3R #H4R #L1 #L2 #T #H
lapply (s_rs_transitive_lex_inv_isid … H3R) -H3R #H3R
@(tc_lfxs_ind_sn … H1R … H) -H -L2