+++ /dev/null
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-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
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-
-include "basic_2/substitution/cpye_cpye.ma".
-include "basic_2/reduction/lpx_cpys.ma".
-
-axiom cpx_cpys_conf_lpx: ∀h,g,G,d,e.
- ∀L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ➡[h, g] T1 → ∀L1. ⦃G, L0⦄ ⊢ ➡[h, g] L1 →
- ∀T2. ⦃G, L0⦄ ⊢ T0 ▶*[d, e] T2 →
- ∃∃T. ⦃G, L1⦄ ⊢ T1 ▶*[d, e] T & ⦃G, L0⦄ ⊢ T2 ➡[h, g] T.
-
-(* SN EXTENDED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS *********************)
-
-(* Forward lemmas on evaluation for extended substitution *******************)
-
-lemma cpx_cpys_cpye_fwd_lpx: ∀h,g,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2 →
- ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 →
- ∀U1,d,e. ⦃G, L1⦄ ⊢ T1 ▶*[d, e] U1 →
- ∀U2. ⦃G, L2⦄ ⊢ T2 ▶*[d, e] 𝐍⦃U2⦄ →
- ⦃G, L1⦄ ⊢ U1 ➡[h, g] U2.
-#h #g #G #L1 #T1 #T2 #HT12 #L2 #HL12 #U1 #d #e #HTU1
-elim (cpx_cpys_conf_lpx … HT12 … HL12 … HTU1) -T1
-/3 width=9 by cpx_cpys_trans_lpx, cpye_cpys_conf/
-qed-.
-
-lemma cpx_cpye_fwd_lpx: ∀h,g,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2 →
- ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 →
- ∀U1,d,e. ⦃G, L1⦄ ⊢ T1 ▶*[d, e] 𝐍⦃U1⦄ →
- ∀U2. ⦃G, L2⦄ ⊢ T2 ▶*[d, e] 𝐍⦃U2⦄ →
- ⦃G, L1⦄ ⊢ U1 ➡[h, g] U2.
-#h #g #G #L1 #T1 #T2 #HT12 #L2 #HL12 #U1 #d #e *
-/2 width=9 by cpx_cpys_cpye_fwd_lpx/
-qed-.