(* Advanced properties ******************************************************)
-lemma cpm_sort_iter (h) (G) (L):
- ∀n. n ≤ 1 →
- ∀s. ⦃G,L⦄ ⊢ ⋆s ➡ [n,h] ⋆((next h)^n s).
+lemma cpm_sort (h) (G) (L):
+ ∀n. n ≤ 1 → ∀s. ⦃G,L⦄ ⊢ ⋆s ➡[n,h] ⋆((next h)^n s).
#h #G #L * //
#n #H #s <(le_n_O_to_eq n) /2 width=1 by le_S_S_to_le/
qed.
]
qed-.
+lemma cpm_inv_abst_bi: ∀n,h,p1,p2,G,L,V1,V2,T1,T2. ⦃G,L⦄ ⊢ ⓛ{p1}V1.T1 ➡[n,h] ⓛ{p2}V2.T2 →
+ ∧∧ ⦃G,L⦄ ⊢ V1 ➡[h] V2 & ⦃G,L.ⓛV1⦄ ⊢ T1 ➡[n,h] T2 & p1 = p2.
+#n #h #p1 #p2 #G #L #V1 #V2 #T1 #T2 #H
+elim (cpm_inv_abst1 … H) -H #XV #XT #HV #HT #H destruct
+/2 width=1 by and3_intro/
+qed-.
+
(* Basic_1: includes: pr0_gen_appl pr2_gen_appl *)
(* Basic_2A1: includes: cpr_inv_appl1 *)
lemma cpm_inv_appl1: ∀n,h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓐ V1.U1 ➡[n, h] U2 →
]
qed-.
+(* Advanced inversion lemmas ************************************************)
+
+lemma cpm_inv_appl_sn_decompose (h) (n) (G) (L) (V1) (T1):
+ ∀X2. ⦃G,L⦄ ⊢ ⓐV1.T1 ➡[n,h] X2 →
+ ∃∃T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 & ⦃G,L⦄ ⊢ ⓐV1.T2 ➡[h] X2.
+#h #n #G #L #V1 #T1 #X2 #H
+elim (cpm_inv_appl1 … H) -H *
+[ #V2 #T2 #HV12 #HT12 #H destruct
+ /3 width=3 by cpm_appl, ex2_intro/
+| #p #V2 #W1 #W2 #U1 #U2 #HV12 #HW12 #HU12 #H1 #H2 destruct
+ /3 width=5 by cpm_beta, cpm_bind, ex2_intro/
+| #p #V2 #V0 #W1 #W2 #U1 #U2 #HV12 #HV20 #HW12 #HU12 #H1 #H2 destruct
+ /3 width=5 by cpm_theta, cpm_bind, ex2_intro/
+]
+qed-.
+
(* Basic forward lemmas *****************************************************)
(* Basic_2A1: includes: cpr_fwd_bind1_minus *)