(* Basic_1: uses: pr3_pr2_pr2_t *)
(* Basic_1: includes: pr3_pr0_pr2_t *)
-lemma lpr_cpr_trans (h) (G): s_r_transitive … (λL. cpm h G L 0) (λ_. lpr h G).
+lemma lpr_cpr_trans (h) (G):
+ s_r_transitive … (λL. cpm h G L 0) (λ_. lpr h 0 G).
/3 width=4 by cprs_inv_CTC, lpr_cpm_trans, ltc_inv_CTC/
qed-.
(* Basic_1: uses: pr3_pr2_pr3_t pr3_wcpr0_t *)
-lemma lpr_cprs_trans (h) (G): s_rs_transitive … (λL. cpm h G L 0) (λ_. lpr h G).
+lemma lpr_cprs_trans (h) (G):
+ s_rs_transitive … (λL. cpm h G L 0) (λ_. lpr h 0 G).
#h #G @s_r_trans_CTC1 /2 width=3 by lpr_cpr_trans/ (**) (* full auto fails *)
qed-.
lemma cprs_lpr_conf_dx (h) (G):
- ∀L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ➡*[h] T1 → ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 →
- ∃∃T. ⦃G,L1⦄ ⊢ T1 ➡*[h] T & ⦃G,L1⦄ ⊢ T0 ➡*[h] T.
+ ∀L0,T0,T1. ❨G,L0❩ ⊢ T0 ➡*[h,0] T1 → ∀L1. ❨G,L0❩ ⊢ ➡[h,0] L1 →
+ ∃∃T. ❨G,L1❩ ⊢ T1 ➡*[h,0] T & ❨G,L1❩ ⊢ T0 ➡*[h,0] T.
#h #G #L0 #T0 #T1 #H
@(cprs_ind_dx … H) -T1 /2 width=3 by ex2_intro/
#T #T1 #_ #HT1 #IHT0 #L1 #HL01
qed-.
lemma cprs_lpr_conf_sn (h) (G):
- ∀L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ➡*[h] T1 →
- ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 →
- ∃∃T. ⦃G,L0⦄ ⊢ T1 ➡*[h] T & ⦃G,L1⦄ ⊢ T0 ➡*[h] T.
+ ∀L0,T0,T1. ❨G,L0❩ ⊢ T0 ➡*[h,0] T1 →
+ ∀L1. ❨G,L0❩ ⊢ ➡[h,0] L1 →
+ ∃∃T. ❨G,L0❩ ⊢ T1 ➡*[h,0] T & ❨G,L1❩ ⊢ T0 ➡*[h,0] T.
#h #G #L0 #T0 #T1 #HT01 #L1 #HL01
elim (cprs_lpr_conf_dx … HT01 … HL01) -HT01 #T #HT1 #HT0
/3 width=3 by lpr_cpms_trans, ex2_intro/