1 include "basic_2/dynamic/cnv_cpce.ma".
3 lemma pippo (h) (a) (G) (L0):
4 ∀T0. ⦃G,L0⦄ ⊢ T0 ![h,a] →
5 ∀n,T1. ⦃G,L0⦄ ⊢ T0 ➡[n,h] T1 → ∀T2. ⦃G,L0⦄ ⊢ T0 ⬌η[h] T2 →
6 ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 →
7 ∃∃T. ⦃G,L1⦄ ⊢ T1 ⬌η[h] T & ⦃G,L0⦄ ⊢ T2 ➡[n,h] T.
9 [ #s #_ #n #X1 #HX1 #X2 #HX2 #L1 #HL01
10 elim (cpm_inv_sort1 … HX1) -HX1 #H #Hn destruct
11 lapply (cpce_inv_sort_sn … HX2) -HX2 #H destruct
12 /3 width=3 by cpce_sort, cpm_sort, ex2_intro/
13 | #i #_ #n #X1 #HX1 #X2 #HX2 #L1 #HL01
14 elim (drops_F_uni L0 i)
19 lemma cpce_inv_eta_drops (h) (n) (G) (L) (i):
20 ∀X. ⦃G,L⦄ ⊢ #i ⬌η[h] X →
21 ∀K,W. ⇩*[i] L ≘ K.ⓛW →
22 ∀p,V1,U. ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V1.U →
23 ∀V2. ⦃G,K⦄ ⊢ V1 ⬌η[h] V2 →
24 ∀W2. ⇧*[↑i] V2 ≘ W2 → X = +ⓛW2.ⓐ#0.#↑i.
26 theorem cpce_mono_cnv (h) (a) (G) (L):
27 ∀T. ⦃G,L⦄ ⊢ T ![h,a] →
28 ∀T1. ⦃G,L⦄ ⊢ T ⬌η[h] T1 → ∀T2. ⦃G,L⦄ ⊢ T ⬌η[h] T2 → T1 = T2.