qed.
lemma cpxs_zeta (h) (G) (L) (V):
- â\88\80T1,T. â¬\86*[1] T ≘ T1 →
+ â\88\80T1,T. â\87§*[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):
- â\88\80T2,T. â¬\86*[1] T2 ≘ T →
+ â\88\80T2,T. â\87§*[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.
- â¦\83G,Lâ¦\84 â\8a¢ V1 â¬\88[h] V â\86\92 â¬\86*[1] V ≘ V2 → ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈*[h] T2 →
+ â¦\83G,Lâ¦\84 â\8a¢ V1 â¬\88[h] V â\86\92 â\87§*[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/