(* Basic_2A1: includes: lpx_sn_conf *)
theorem lexs_conf (RN1) (RP1) (RN2) (RP2):
∀L,f.
- (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V → ⫱*[n] f = ⫯g → lexs_pw_confluent2_R RN1 RN2 RN1 RP1 RN2 RP2 g K V) →
- (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V → ⫱*[n] f = ↑g → lexs_pw_confluent2_R RP1 RP2 RN1 RP1 RN2 RP2 g K V) →
+ (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V → ⫯g = ⫱*[n] f → lexs_pw_confluent2_R RN1 RN2 RN1 RP1 RN2 RP2 g K V) →
+ (∀g,I,K,V,n. ⬇*[n] L ≡ K.ⓑ{I}V → ↑g = ⫱*[n] f → lexs_pw_confluent2_R RP1 RP2 RN1 RP1 RN2 RP2 g K V) →
pw_confluent2 … (lexs RN1 RP1 f) (lexs RN2 RP2 f) L.
#RN1 #RP1 #RN2 #RP2 #L elim L -L
[ #f #_ #_ #L1 #H1 #L2 #H2 >(lexs_inv_atom1 … H1) >(lexs_inv_atom1 … H2) -H2 -H1