(* Basic_2A1: uses: TC_lpx_sn_pair TC_lpx_sn_pair_refl *)
lemma rexs_pair_refl: ∀R. c_reflexive … R →
- ∀L,V1,V2. CTC … R L V1 V2 → ∀I,T. L.ⓑ{I}V1 ⪤*[R,T] L.ⓑ{I}V2.
+ ∀L,V1,V2. CTC … R L V1 V2 → ∀I,T. L.ⓑ[I]V1 ⪤*[R,T] L.ⓑ[I]V2.
#R #HR #L #V1 #V2 #H elim H -V2
/3 width=3 by rexs_step_dx, rex_pair_refl, inj/
qed.
-lemma rexs_tc: â\88\80R,L1,L2,T,f. ð\9d\90\88â¦\83fâ¦\84 → TC … (sex cfull (cext2 R) f) L1 L2 →
+lemma rexs_tc: â\88\80R,L1,L2,T,f. ð\9d\90\88â\9dªfâ\9d« → TC … (sex cfull (cext2 R) f) L1 L2 →
L1 ⪤*[R,T] L2.
#R #L1 #L2 #T #f #Hf #H elim H -L2
[ elim (frees_total L1 T) | #L elim (frees_total L T) ]
(* Advanced inversion lemmas ************************************************)
lemma rexs_inv_bind_void: ∀R. c_reflexive … R →
- ∀p,I,L1,L2,V,T. L1 ⪤*[R,ⓑ{p,I}V.T] L2 →
+ ∀p,I,L1,L2,V,T. L1 ⪤*[R,ⓑ[p,I]V.T] L2 →
∧∧ L1 ⪤*[R,V] L2 & L1.ⓧ ⪤*[R,T] L2.ⓧ.
#R #HR #p #I #L1 #L2 #V #T #H @(rexs_ind_sn … HR … H) -L2
[ /3 width=1 by rexs_refl, conj/
(* Advanced forward lemmas **************************************************)
lemma rexs_fwd_bind_dx_void: ∀R. c_reflexive … R →
- ∀p,I,L1,L2,V,T. L1 ⪤*[R,ⓑ{p,I}V.T] L2 →
+ ∀p,I,L1,L2,V,T. L1 ⪤*[R,ⓑ[p,I]V.T] L2 →
L1.ⓧ ⪤*[R,T] L2.ⓧ.
#R #HR #p #I #L1 #L2 #V #T #H elim (rexs_inv_bind_void … H) -H //
qed-.