(* Properties with generic slicing for local environments *******************)
-(* Note: the premise ð\9d\90\94â¦\83fâ¦\84 cannot be removed *)
+(* Note: the premise ð\9d\90\94â\9dªfâ\9d« cannot be removed *)
(* Basic_2A1: includes: lsubsv_drop_O1_conf *)
-lemma lsubv_drops_conf_isuni (a) (h) (G):
- ∀L1,L2. G ⊢ L1 ⫃![a,h] L2 →
- ∀b,f,K1. 𝐔⦃f⦄ → ⬇*[b,f] L1 ≘ K1 →
- ∃∃K2. G ⊢ K1 ⫃![a,h] K2 & ⬇*[b,f] L2 ≘ K2.
-#a #h #G #L1 #L2 #H elim H -L1 -L2
+lemma lsubv_drops_conf_isuni (h) (a) (G):
+ ∀L1,L2. G ⊢ L1 ⫃![h,a] L2 →
+ ∀b,f,K1. 𝐔❪f❫ → ⇩*[b,f] L1 ≘ K1 →
+ ∃∃K2. G ⊢ K1 ⫃![h,a] K2 & ⇩*[b,f] L2 ≘ 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 *
]
qed-.
-(* Note: the premise ð\9d\90\94â¦\83fâ¦\84 cannot be removed *)
+(* Note: the premise ð\9d\90\94â\9dªfâ\9d« cannot be removed *)
(* Basic_2A1: includes: lsubsv_drop_O1_trans *)
-lemma lsubv_drops_trans_isuni (a) (h) (G):
- ∀L1,L2. G ⊢ L1 ⫃![a,h] L2 →
- ∀b,f,K2. 𝐔⦃f⦄ → ⬇*[b,f] L2 ≘ K2 →
- ∃∃K1. G ⊢ K1 ⫃![a,h] K2 & ⬇*[b,f] L1 ≘ K1.
-#a #h #G #L1 #L2 #H elim H -L1 -L2
+lemma lsubv_drops_trans_isuni (h) (a) (G):
+ ∀L1,L2. G ⊢ L1 ⫃![h,a] L2 →
+ ∀b,f,K2. 𝐔❪f❫ → ⇩*[b,f] L2 ≘ K2 →
+ ∃∃K1. G ⊢ K1 ⫃![h,a] K2 & ⇩*[b,f] L1 ≘ 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 *