qed.
lemma cpms_zeta (n) (h) (G) (L):
- â\88\80T1,T. â¬\86*[1] T ≘ T1 →
+ â\88\80T1,T. â\87§*[1] T ≘ T1 →
∀V,T2. ⦃G,L⦄ ⊢ T ➡*[n,h] T2 → ⦃G,L⦄ ⊢ +ⓓV.T1 ➡*[n,h] T2.
#n #h #G #L #T1 #T #HT1 #V #T2 #H @(cpms_ind_dx … H) -T2
/3 width=3 by cpms_step_dx, cpm_cpms, cpm_zeta/
(* Basic_2A1: uses: cprs_zeta *)
lemma cpms_zeta_dx (n) (h) (G) (L):
- â\88\80T2,T. â¬\86*[1] T2 ≘ T →
+ â\88\80T2,T. â\87§*[1] T2 ≘ T →
∀V,T1. ⦃G,L.ⓓV⦄ ⊢ T1 ➡*[n,h] T → ⦃G,L⦄ ⊢ +ⓓV.T1 ➡*[n,h] T2.
#n #h #G #L #T2 #T #HT2 #V #T1 #H @(cpms_ind_sn … H) -T1
/3 width=3 by cpms_step_sn, cpm_cpms, cpm_bind, cpm_zeta/
(* Basic_2A1: uses: cprs_theta_dx *)
lemma cpms_theta_dx (n) (h) (G) (L):
∀V1,V. ⦃G,L⦄ ⊢ V1 ➡[h] V →
- â\88\80V2. â¬\86*[1] V ≘ V2 →
+ â\88\80V2. â\87§*[1] V ≘ V2 →
∀W1,W2. ⦃G,L⦄ ⊢ W1 ➡[h] W2 →
∀T1,T2. ⦃G,L.ⓓW1⦄ ⊢ T1 ➡*[n,h] T2 →
∀p. ⦃G,L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ➡*[n,h] ⓓ{p}W2.ⓐV2.T2.