lemma cpms_inv_abbr_sn_dx (n) (h) (G) (L):
∀p,V1,T1,X2. ⦃G,L⦄ ⊢ ⓓ{p}V1.T1 ➡*[n,h] X2 →
∨∨ ∃∃V2,T2. ⦃G,L⦄ ⊢ V1 ➡*[h] V2 & ⦃G,L.ⓓV1⦄ ⊢ T1 ➡*[n,h] T2 & X2 = ⓓ{p}V2.T2
- | â\88\83â\88\83T2. â¦\83G,L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡*[n ,h] T2 & â¬\86*[1] X2 ≘ T2 & p = Ⓣ.
+ | â\88\83â\88\83T2. â¦\83G,L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡*[n ,h] T2 & â\87§*[1] X2 ≘ T2 & p = Ⓣ.
#n #h #G #L #p #V1 #T1 #X2 #H
@(cpms_ind_dx … H) -X2 -n /3 width=5 by ex3_2_intro, or_introl/
#n1 #n2 #X #X2 #_ * *
(* Basic_2A1: uses: scpds_inv_abbr_abst *)
lemma cpms_inv_abbr_abst (n) (h) (G) (L):
∀p1,p2,V1,W2,T1,T2. ⦃G,L⦄ ⊢ ⓓ{p1}V1.T1 ➡*[n,h] ⓛ{p2}W2.T2 →
- â\88\83â\88\83T. â¦\83G,L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡*[n,h] T & â¬\86*[1] ⓛ{p2}W2.T2 ≘ T & p1 = Ⓣ.
+ â\88\83â\88\83T. â¦\83G,L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡*[n,h] T & â\87§*[1] ⓛ{p2}W2.T2 ≘ T & p1 = Ⓣ.
#n #h #G #L #p1 #p2 #V1 #W2 #T1 #T2 #H
elim (cpms_inv_abbr_sn_dx … H) -H *
[ #V #T #_ #_ #H destruct