(* *)
(**************************************************************************)
-include "basic_2/rt_transition/lpr_lpr.ma".
include "basic_2/rt_computation/cpms_lpr.ma".
include "basic_2/rt_computation/cprs_cpr.ma".
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] T1 → ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 →
+ ∃∃T. ⦃G,L1⦄ ⊢ T1 ➡*[h] T & ⦃G,L1⦄ ⊢ T0 ➡*[h] 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] T1 →
+ ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 →
+ ∃∃T. ⦃G,L0⦄ ⊢ T1 ➡*[h] T & ⦃G,L1⦄ ⊢ T0 ➡*[h] 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/