(* Note: the premise đâŚf⌠cannot be removed *)
(* Basic_2A1: includes: lsubsv_drop_O1_conf *)
lemma lsubv_drops_conf_isuni (a) (h) (G):
- âL1,L2. G ⢠L1 âŤ![a,h] L2 â
- âb,f,K1. đâŚf⌠â âŹ*[b,f] L1 â K1 â
- ââK2. G ⢠K1 âŤ![a,h] K2 & âŹ*[b,f] L2 â K2.
+ âL1,L2. G ⢠L1 âŤ![a,h] L2 â
+ âb,f,K1. đâŚf⌠â âŹ*[b,f] L1 â K1 â
+ ââK2. G ⢠K1 âŤ![a,h] K2 & âŹ*[b,f] L2 â K2.
#a #h #G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3 by ex2_intro/
| #I #L1 #L2 #HL12 #IH #b #f #K1 #Hf #H
(* Note: the premise đâŚf⌠cannot be removed *)
(* Basic_2A1: includes: lsubsv_drop_O1_trans *)
lemma lsubv_drops_trans_isuni (a) (h) (G):
- âL1,L2. G ⢠L1 âŤ![a,h] L2 â
- âb,f,K2. đâŚf⌠â âŹ*[b,f] L2 â K2 â
- ââK1. G ⢠K1 âŤ![a,h] K2 & âŹ*[b,f] L1 â K1.
+ âL1,L2. G ⢠L1 âŤ![a,h] L2 â
+ âb,f,K2. đâŚf⌠â âŹ*[b,f] L2 â K2 â
+ ââK1. G ⢠K1 âŤ![a,h] K2 & âŹ*[b,f] L1 â K1.
#a #h #G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3 by ex2_intro/
| #I #L1 #L2 #HL12 #IH #b #f #K2 #Hf #H