(* Note: the premise đâŠf⊠cannot be removed *)
(* Basic_2A1: includes: lsubsv_drop_O1_conf *)
-lemma lsubv_drops_conf_isuni (a) (h) (G):
- âL1,L2. G âą L1 â«![a,h] L2 â
- âb,f,K1. đâŠf⊠â âŹ*[b,f] L1 â K1 â
- ââK2. G âą K1 â«![a,h] K2 & âŹ*[b,f] L2 â K2.
-#a #h #G #L1 #L2 #H elim H -L1 -L2
+lemma lsubv_drops_conf_isuni (h) (a) (G):
+ âL1,L2. G âą L1 â«![h,a] L2 â
+ âb,f,K1. đâŠf⊠â â©*[b,f] L1 â K1 â
+ ââK2. G âą K1 â«![h,a] K2 & â©*[b,f] L2 â K2.
+#h #a #G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3 by ex2_intro/
| #I #L1 #L2 #HL12 #IH #b #f #K1 #Hf #H
elim (drops_inv_bind1_isuni ⊠Hf H) -Hf -H *
(* Note: the premise đâŠf⊠cannot be removed *)
(* Basic_2A1: includes: lsubsv_drop_O1_trans *)
-lemma lsubv_drops_trans_isuni (a) (h) (G):
- âL1,L2. G âą L1 â«![a,h] L2 â
- âb,f,K2. đâŠf⊠â âŹ*[b,f] L2 â K2 â
- ââK1. G âą K1 â«![a,h] K2 & âŹ*[b,f] L1 â K1.
-#a #h #G #L1 #L2 #H elim H -L1 -L2
+lemma lsubv_drops_trans_isuni (h) (a) (G):
+ âL1,L2. G âą L1 â«![h,a] L2 â
+ âb,f,K2. đâŠf⊠â â©*[b,f] L2 â K2 â
+ ââK1. G âą K1 â«![h,a] K2 & â©*[b,f] L1 â K1.
+#h #a #G #L1 #L2 #H elim H -L1 -L2
[ /2 width=3 by ex2_intro/
| #I #L1 #L2 #HL12 #IH #b #f #K2 #Hf #H
elim (drops_inv_bind1_isuni ⊠Hf H) -Hf -H *