lemma sex_sdj_split_dx (R1) (R2) (RP):
c_reflexive … R1 → c_reflexive … R2 → c_reflexive … RP →
∀L1,f1.
- (â\88\80g,I,K,n. â\87©[n] L1 â\89\98 K.â\93\98[I] â\86\92 â\86\91g = ⫱*[n] f1 → R_pw_confluent1_sex R1 R1 R2 cfull g K I) →
+ (â\88\80g,I,K,n. â\87©[n] L1 â\89\98 K.â\93\98[I] â\86\92 â\86\91g = â«°*[n] f1 → R_pw_confluent1_sex R1 R1 R2 cfull g K I) →
∀L2. L1 ⪤[R1,RP,f1] L2 → ∀f2. f1 ∥ f2 →
∃∃L. L1 ⪤[R2,cfull,f1] L & L ⪤[RP,R1,f2] L2.
#R1 #R2 #RP #HR1 #HR2 #HRP #L1 elim L1 -L1