elim (simple_inv_bind … HT1)
]
qed-.
-
+
+(* Advanced forward lemmas **************************************************)
+
+lemma cpr_fwd_abst1: ∀a,L,V1,T1,U2. L ⊢ ⓛ{a}V1.T1 ➡ U2 → ∀b,I,W.
+ ∃∃V2,T2. L ⊢ ⓑ{b,I}W.T1 ➡ ⓑ{b,I}W.T2 &
+ U2 = ⓛ{a}V2.T2.
+#a #L #V1 #T1 #U2 * #U #H #HU2 #b #I #W
+elim (tpr_fwd_abst1 … H b I W) -H #V #T #HT1 #H destruct
+elim (tpss_inv_bind1 … HU2) -HU2 #V2 #T2 #_ #HT2
+lapply (tpss_lsubs_trans … HT2 (L.ⓑ{I}W) ?) -HT2 /2 width=1/ /4 width=5/
+qed-.
+
(* Relocation properties ****************************************************)
(* Basic_1: was: pr2_lift *)
#L #K #d #e #HLK #T1 #U1 #HTU1 #U2 * #U #HU1 #HU2
elim (tpr_inv_lift1 … HU1 … HTU1) -U1 #T #HTU #T1
elim (lt_or_ge (|L|) d) #HLd
-[ elim (tpss_inv_lift1_le … HU2 … HLK … HTU ?) -U -HLK [ /5 width=4/ | /2 width=2/ ]
+[ elim (tpss_inv_lift1_le … HU2 … HLK … HTU ?) -U -HLK /2 width=2/
+ /3 width=7 by ex2_intro, cpr_intro/
| elim (lt_or_ge (|L|) (d + e)) #HLde
- [ elim (tpss_inv_lift1_be_up … HU2 … HLK … HTU ? ?) -U -HLK // [ /5 width=4/ | /2 width=2/ ]
- | elim (tpss_inv_lift1_be … HU2 … HLK … HTU ? ?) -U -HLK // /5 width=4/
+ [ elim (tpss_inv_lift1_be_up … HU2 … HLK … HTU ? ?) -U -HLK // /2 width=2/
+ /3 width=7 by ex2_intro, cpr_intro/
+ | elim (tpss_inv_lift1_be … HU2 … HLK … HTU ? ?) -U -HLK //
+ /3 width=7 by ex2_intro, cpr_intro/
]
]
qed.