(* Basic_1: was just: sn3_lift *)
lemma csx_lift: ∀h,g,G,L2,L1,T1,s,d,e. ⦃G, L1⦄ ⊢ ⬊*[h, g] T1 →
- â\88\80T2. â\87©[s, d, e] L2 â\89¡ L1 â\86\92 â\87§[d, e] T1 ≡ T2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T2.
+ â\88\80T2. â¬\87[s, d, e] L2 â\89¡ L1 â\86\92 â¬\86[d, e] T1 ≡ T2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T2.
#h #g #G #L2 #L1 #T1 #s #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL21 #HT12
@csx_intro #T #HLT2 #HT2
elim (cpx_inv_lift1 … HLT2 … HL21 … HT12) -HLT2 #T0 #HT0 #HLT10
(* Basic_1: was just: sn3_gen_lift *)
lemma csx_inv_lift: ∀h,g,G,L2,L1,T1,s,d,e. ⦃G, L1⦄ ⊢ ⬊*[h, g] T1 →
- â\88\80T2. â\87©[s, d, e] L1 â\89¡ L2 â\86\92 â\87§[d, e] T2 ≡ T1 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T2.
+ â\88\80T2. â¬\87[s, d, e] L1 â\89¡ L2 â\86\92 â¬\86[d, e] T2 ≡ T1 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T2.
#h #g #G #L2 #L1 #T1 #s #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21
@csx_intro #T #HLT2 #HT2
elim (lift_total T d e) #T0 #HT0
(* Advanced inversion lemmas ************************************************)
(* Basic_1: was: sn3_gen_def *)
-lemma csx_inv_lref_bind: â\88\80h,g,I,G,L,K,V,i. â\87©[i] L ≡ K.ⓑ{I}V →
+lemma csx_inv_lref_bind: â\88\80h,g,I,G,L,K,V,i. â¬\87[i] L ≡ K.ⓑ{I}V →
⦃G, L⦄ ⊢ ⬊*[h, g] #i → ⦃G, K⦄ ⊢ ⬊*[h, g] V.
#h #g #I #G #L #K #V #i #HLK #Hi
elim (lift_total V 0 (i+1))
(* Advanced properties ******************************************************)
(* Basic_1: was just: sn3_abbr *)
-lemma csx_lref_bind: â\88\80h,g,I,G,L,K,V,i. â\87©[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ ⬊*[h, g] V → ⦃G, L⦄ ⊢ ⬊*[h, g] #i.
+lemma csx_lref_bind: â\88\80h,g,I,G,L,K,V,i. â¬\87[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ ⬊*[h, g] V → ⦃G, L⦄ ⊢ ⬊*[h, g] #i.
#h #g #I #G #L #K #V #i #HLK #HV
@csx_intro #X #H #Hi
elim (cpx_inv_lref1 … H) -H