(* Properties on relocation *************************************************)
(* Basic_1: was just: sty0_lift *)
-lemma ssta_lift: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
+lemma ssta_lift: ∀h,g,L1,T1,U1,l. ⦃h, L1⦄ ⊢ T1 •[h, g] ⦃l, U1⦄ →
∀L2,d,e. ⇩[d, e] L2 ≡ L1 → ∀T2. ⇧[d, e] T1 ≡ T2 →
- ∀U2. ⇧[d, e] U1 ≡ U2 → ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄.
+ ∀U2. ⇧[d, e] U1 ≡ U2 → ⦃h, L2⦄ ⊢ T2 •[h, g] ⦃l, U2⦄.
#h #g #L1 #T1 #U1 #l #H elim H -L1 -T1 -U1 -l
[ #L1 #k #l #Hkl #L2 #d #e #HL21 #X1 #H1 #X2 #H2
>(lift_inv_sort1 … H1) -X1
qed.
(* Note: apparently this was missing in basic_1 *)
-lemma ssta_inv_lift1: ∀h,g,L2,T2,U2,l. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ →
+lemma ssta_inv_lift1: ∀h,g,L2,T2,U2,l. ⦃h, L2⦄ ⊢ T2 •[h, g] ⦃l, U2⦄ →
∀L1,d,e. ⇩[d, e] L2 ≡ L1 → ∀T1. ⇧[d, e] T1 ≡ T2 →
- ∃∃U1. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ & ⇧[d, e] U1 ≡ U2.
+ ∃∃U1. ⦃h, L1⦄ ⊢ T1 •[h, g] ⦃l, U1⦄ & ⇧[d, e] U1 ≡ U2.
#h #g #L2 #T2 #U2 #l #H elim H -L2 -T2 -U2 -l
[ #L2 #k #l #Hkl #L1 #d #e #_ #X #H
>(lift_inv_sort2 … H) -X /3 width=3/
(* Advanced forvard lemmas **************************************************)
(* Basic_1: was just: sty0_correct *)
-lemma ssta_fwd_correct: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ →
- ∃T0. ⦃h, L⦄ ⊢ U •[g] ⦃l-1, T0⦄.
+lemma ssta_fwd_correct: ∀h,g,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U⦄ →
+ ∃T0. ⦃G, L⦄ ⊢ U •[h, g] ⦃l-1, T0⦄.
#h #g #L #T #U #l #H elim H -L -T -U -l
[ /4 width=2/
| #L #K #V #W #W0 #i #l #HLK #_ #HW0 * #V0 #HWV0