qed-.
(* Note: probably this is an inversion lemma *)
-lemma cpxs_fwd_delta: â\88\80h,g,I,G,L,K,V1,i. â\87©[i] L ≡ K.ⓑ{I}V1 →
- â\88\80V2. â\87§[0, i + 1] V1 ≡ V2 →
+lemma cpxs_fwd_delta: â\88\80h,g,I,G,L,K,V1,i. â¬\87[i] L ≡ K.ⓑ{I}V1 →
+ â\88\80V2. â¬\86[0, i + 1] V1 ≡ V2 →
∀U. ⦃G, L⦄ ⊢ #i ➡*[h, g] U →
#i ≂ U ∨ ⦃G, L⦄ ⊢ V2 ➡*[h, g] U.
#h #g #I #G #L #K #V1 #i #HLK #V2 #HV12 #U #H
qed-.
lemma cpxs_fwd_theta: ∀h,g,a,G,L,V1,V,T,U. ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}V.T ➡*[h, g] U →
- â\88\80V2. â\87§[0, 1] V1 ≡ V2 → ⓐV1.ⓓ{a}V.T ≂ U ∨
+ â\88\80V2. â¬\86[0, 1] V1 ≡ V2 → ⓐV1.ⓓ{a}V.T ≂ U ∨
⦃G, L⦄ ⊢ ⓓ{a}V.ⓐV2.T ➡*[h, g] U.
#h #g #a #G #L #V1 #V #T #U #H #V2 #HV12
elim (cpxs_inv_appl1 … H) -H *