(* Advanced properties ******************************************************)
lemma cpr_cdelta: ∀L,K,V1,W1,W2,i.
- ⇩[0, i] L ≡ K. ⓓV1 → K ⊢ V1 [0, |L| - i - 1] ▶* W1 →
+ ⇩[0, i] L ≡ K. ⓓV1 → K ⊢ V1 ▶* [0, |L| - i - 1] W1 →
⇧[0, i + 1] W1 ≡ W2 → L ⊢ #i ➡ W2.
#L #K #V1 #W1 #W2 #i #HLK #HVW1 #HW12
lapply (ldrop_fwd_ldrop2_length … HLK) #Hi
@ex2_1_intro [2: // | skip | @tpss_subst /width=6/ ] (**) (* /3 width=6/ is too slow *)
qed.
+lemma cpr_abst: ∀L,V1,V2. L ⊢ V1 ➡ V2 → ∀V,T1,T2.
+ L.ⓛV ⊢ T1 ➡ T2 → L ⊢ ⓛV1. T1 ➡ ⓛV2. T2.
+#L #V1 #V2 * #V0 #HV10 #HV02 #V #T1 #T2 * #T0 #HT10 #HT02
+lapply (tpss_inv_S2 … HT02 L V ?) -HT02 // #HT02
+@(ex2_1_intro … (ⓛV0.T0)) /2 width=1/ -V1 -T1 (**) (* explicit constructors *)
+@tpss_bind // -V0
+@(tpss_lsubs_conf (L.ⓛV)) // -T0 -T2 /2 width=1/
+qed.
+
(* Advanced inversion lemmas ************************************************)
(* Basic_1: was: pr2_gen_lref *)
lemma cpr_inv_lref1: ∀L,T2,i. L ⊢ #i ➡ T2 →
T2 = #i ∨
∃∃K,V1,T1. ⇩[0, i] L ≡ K. ⓓV1 &
- K ⊢ V1 [0, |L| - i - 1] ▶* T1 &
+ K ⊢ V1 ▶* [0, |L| - i - 1] T1 &
⇧[0, i + 1] T1 ≡ T2 &
i < |L|.
#L #T2 #i * #X #H
qed-.
(* Note: the main property of simple terms *)
-lemma cpr_inv_appl1_simple: ∀L,V1,T1,U. L ⊢ ⓐV1. T1 ➡ U → 𝐒[T1] →
+lemma cpr_inv_appl1_simple: ∀L,V1,T1,U. L ⊢ ⓐV1. T1 ➡ U → 𝐒⦃T1⦄ →
∃∃V2,T2. L ⊢ V1 ➡ V2 & L ⊢ T1 ➡ T2 &
U = ⓐV2. T2.
#L #V1 #T1 #U #H #HT1