qed.
lemma cpxs_zeta (h) (G) (L) (V):
- ∀T1,T. ⇧*[1] T ≘ T1 →
+ ∀T1,T. ⇧[1] T ≘ T1 →
∀T2. ❪G,L❫ ⊢ T ⬈*[h] T2 → ❪G,L❫ ⊢ +ⓓV.T1 ⬈*[h] T2.
#h #G #L #V #T1 #T #HT1 #T2 #H @(cpxs_ind … H) -T2
/3 width=3 by cpxs_strap1, cpx_cpxs, cpx_zeta/
(* Basic_2A1: was: cpxs_zeta *)
lemma cpxs_zeta_dx (h) (G) (L) (V):
- ∀T2,T. ⇧*[1] T2 ≘ T →
+ ∀T2,T. ⇧[1] T2 ≘ T →
∀T1. ❪G,L.ⓓV❫ ⊢ T1 ⬈*[h] T → ❪G,L❫ ⊢ +ⓓV.T1 ⬈*[h] T2.
#h #G #L #V #T2 #T #HT2 #T1 #H @(cpxs_ind_dx … H) -T1
/3 width=3 by cpxs_strap2, cpx_cpxs, cpx_bind, cpx_zeta/
qed.
lemma cpxs_theta_dx: ∀h,p,G,L,V1,V,V2,W1,W2,T1,T2.
- ❪G,L❫ ⊢ V1 ⬈[h] V → ⇧*[1] V ≘ V2 → ❪G,L.ⓓW1❫ ⊢ T1 ⬈*[h] T2 →
+ ❪G,L❫ ⊢ V1 ⬈[h] V → ⇧[1] V ≘ V2 → ❪G,L.ⓓW1❫ ⊢ T1 ⬈*[h] T2 →
❪G,L❫ ⊢ W1 ⬈[h] W2 → ❪G,L❫ ⊢ ⓐV1.ⓓ[p]W1.T1 ⬈*[h] ⓓ[p]W2.ⓐV2.T2.
#h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 * -T2
/4 width=9 by cpx_cpxs, cpxs_strap1, cpxs_bind_dx, cpxs_flat_dx, cpx_theta/