@csn_intro #T #HLT2 #HT2
elim (cpr_inv_lift … HL21 … HT12 … HLT2) -HLT2 #T0 #HT0 #HLT10
@(IHT1 … HLT10) // -L1 -L2 #H destruct
->(lift_mono … HT0 … HT12) in HT2; -T0 /2 width=1/
+>(lift_mono … HT0 … HT12) in HT2; -T1 /2 width=1/
qed.
(* Basic_1: was: sn3_gen_lift *)
elim (lift_total T d e) #T0 #HT0
lapply (cpr_lift … HL12 … HT21 … HT0 HLT2) -HLT2 #HLT10
@(IHT1 … HLT10) // -L1 -L2 #H destruct
->(lift_inj … HT0 … HT21) in HT2; -T0 /2 width=1/
+>(lift_inj … HT0 … HT21) in HT2; -T1 /2 width=1/
qed.
(* Advanced properties ******************************************************)
qed.
lemma csn_appl_simple: ∀L,V. L ⊢ ⬇* V → ∀T1.
- (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → False) → L ⊢ ⬇* ⓐV. T2) →
- 𝐒[T1] → L ⊢ ⬇* ⓐV. T1.
+ (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) → L ⊢ ⬇* ⓐV. T2) →
+ 𝐒⦃T1⦄ → L ⊢ ⬇* ⓐV. T1.
#L #V #H @(csn_ind … H) -V #V #_ #IHV #T1 #IHT1 #HT1
@csn_intro #X #H1 #H2
elim (cpr_inv_appl1_simple … H1 ?) // -H1
]
qed.
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_1: was: sn3_gen_def *)
+lemma csn_inv_lref_abbr: ∀L,K,V,i. ⇩[0, i] L ≡ K. ⓓV → L ⊢ ⬇* #i → K ⊢ ⬇* V.
+#L #K #V #i #HLK #Hi
+elim (lift_total V 0 (i+1)) #V0 #HV0
+lapply (ldrop_fwd_ldrop2 … HLK) #H0LK
+@(csn_inv_lift … H0LK … HV0) -H0LK
+@(csn_cpr_trans … Hi) -Hi /2 width=6/
+qed-.
+
(* Main properties **********************************************************)
theorem csn_acp: acp cpr (eq …) (csn …).