∀f1,K1,K2. K1 ⪤*[RN, RP, f1] K2 →
∀b,f,I1,L1. ⬇*[b, f] L1.ⓘ{I1} ≡ K1 →
∀f2. f ~⊚ f1 ≡ ⫯f2 →
- â\88\83â\88\83I2,L2. â¬\87*[b, f] L2.â\93\98{I2} â\89¡ K2 & L1 ⪤*[RN, RP, f2] L2 & RN L1 I1 I2 & L1.â\93\98{I1} â\89¡[f] L2.ⓘ{I2}.
+ â\88\83â\88\83I2,L2. â¬\87*[b, f] L2.â\93\98{I2} â\89¡ K2 & L1 ⪤*[RN, RP, f2] L2 & RN L1 I1 I2 & L1.â\93\98{I1} â\89\90[f] L2.ⓘ{I2}.
#RN #RP #H1RN #H1RP #H2RN #H2RP #f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
elim (lexs_liftable_co_dedropable_sn … H1RN H1RP H2RN H2RP … HLK1 … HK12 … Hf2) -K1 -f1 -H1RN -H1RP -H2RN -H2RP
#X #HX #HLK2 #H1L12 elim (lexs_inv_next1 … HX) -HX
∀f1,K1,K2. K1 ⪤*[RN, RP, f1] K2 →
∀b,f,I1,L1. ⬇*[b, f] L1.ⓘ{I1} ≡ K1 →
∀f2. f ~⊚ f1 ≡ ↑f2 →
- â\88\83â\88\83I2,L2. â¬\87*[b, f] L2.â\93\98{I2} â\89¡ K2 & L1 ⪤*[RN, RP, f2] L2 & RP L1 I1 I2 & L1.â\93\98{I1} â\89¡[f] L2.ⓘ{I2}.
+ â\88\83â\88\83I2,L2. â¬\87*[b, f] L2.â\93\98{I2} â\89¡ K2 & L1 ⪤*[RN, RP, f2] L2 & RP L1 I1 I2 & L1.â\93\98{I1} â\89\90[f] L2.ⓘ{I2}.
#RN #RP #H1RN #H1RP #H2RN #H2RP #f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
elim (lexs_liftable_co_dedropable_sn … H1RN H1RP H2RN H2RP … HLK1 … HK12 … Hf2) -K1 -f1 -H1RN -H1RP -H2RN -H2RP
#X #HX #HLK2 #H1L12 elim (lexs_inv_push1 … HX) -HX