(* Properties with generic extension of a context sensitive relation ********)
lemma rexs_lex: ∀R. c_reflexive … R →
- ∀L1,L2,T. L1 ⪤[CTC … R] L2 → L1 ⪤*[R, T] L2.
+ ∀L1,L2,T. L1 ⪤[CTC … R] L2 → L1 ⪤*[R,T] L2.
#R #HR #L1 #L2 #T *
/5 width=7 by rexs_tc, sex_inv_tc_dx, sex_co, ext2_inv_tc, ext2_refl/
qed.
lemma rexs_lex_req: ∀R. c_reflexive … R →
∀L1,L. L1 ⪤[CTC … R] L → ∀L2,T. L ≡[T] L2 →
- L1 ⪤*[R, T] L2.
+ L1 ⪤*[R,T] L2.
/3 width=3 by rexs_lex, rexs_step_dx, req_fwd_rex/ qed.
(* Inversion lemmas with generic extension of a context sensitive relation **)
rex_fsge_compatible R →
s_rs_transitive … R (λ_.lex R) →
req_transitive R →
- ∀L1,L2,T. L1 ⪤*[R, T] L2 →
+ ∀L1,L2,T. L1 ⪤*[R,T] L2 →
∃∃L. L1 ⪤[CTC … R] L & L ≡[T] L2.
#R #H1R #H2R #H3R #H4R #L1 #L2 #T #H
lapply (s_rs_transitive_lex_inv_isid … H3R) -H3R #H3R