universary milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lprs_cprs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lprs_cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lprs_cprs.ma
index 9ce393c437959f4b71cba1de7b690709f878dacd..ff82ee0a575821cc667e4378c2d58207af84a51d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lprs_cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lprs_cprs.ma
@@ -35,16 +35,27 @@ lemma lprs_inv_pair2: ∀I,G,L1,K2,V2. ⦃G, L1⦄ ⊢ ➡* K2.ⓑ{I}V2 →
                                L1 = K1.ⓑ{I}V1.
 /3 width=3 by TC_lpx_sn_inv_pair2, lpr_cprs_trans/ qed-.
 
+(* Advanced eliminators *****************************************************)
+
+lemma lprs_ind_alt: ∀G. ∀R:relation lenv.
+                    R (⋆) (⋆) → (
+                       ∀I,K1,K2,V1,V2.
+                       ⦃G, K1⦄ ⊢ ➡* K2 → ⦃G, K1⦄ ⊢ V1 ➡* V2 →
+                       R K1 K2 → R (K1.ⓑ{I}V1) (K2.ⓑ{I}V2)
+                    ) →
+                    ∀L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 → R L1 L2.
+/3 width=4 by TC_lpx_sn_ind, lpr_cprs_trans/ qed-.
+
 (* Properties on context-sensitive parallel computation for terms ***********)
 
-lemma lprs_cpr_trans: ∀G. s_r_transitive … (cpr G) (λ_. lprs G).
-/3 width=5 by s_r_trans_LTC2, lpr_cprs_trans/ qed-.
+lemma lprs_cpr_trans: ∀G. c_r_transitive … (cpr G) (λ_. lprs G).
+/3 width=5 by c_r_trans_LTC2, lpr_cprs_trans/ qed-.
 
 (* Basic_1: was just: pr3_pr3_pr3_t *)
 (* Note: alternative proof /3 width=5 by s_r_trans_LTC1, lprs_cpr_trans/ *)
-lemma lprs_cprs_trans: ∀G. s_rs_transitive … (cpr G) (λ_. lprs G).
-#G @s_r_to_s_rs_trans @s_r_trans_LTC2
-@s_rs_trans_TC1 /2 width=3 by lpr_cprs_trans/ (**) (* full auto too slow *)
+lemma lprs_cprs_trans: ∀G. c_rs_transitive … (cpr G) (λ_. lprs G).
+#G @c_r_to_c_rs_trans @c_r_trans_LTC2
+@c_rs_trans_TC1 /2 width=3 by lpr_cprs_trans/ (**) (* full auto too slow *)
 qed-.
 
 lemma lprs_cprs_conf_dx: ∀G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ➡* T1 →
@@ -106,7 +117,7 @@ lemma cprs_inv_abbr1: ∀a,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{a}V1.T1 ➡* U2 →
                       ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡* V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ➡* T2 &
                                U2 = ⓓ{a}V2.T2
                       ) ∨
-                      â\88\83â\88\83T2. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡* T2 & â\87§[0, 1] U2 ≡ T2 & a = true.
+                      â\88\83â\88\83T2. â¦\83G, L.â\93\93V1â¦\84 â\8a¢ T1 â\9e¡* T2 & â¬\86[0, 1] U2 ≡ T2 & a = true.
 #a #G #L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_introl/
 #U0 #U2 #_ #HU02 * *
 [ #V0 #T0 #HV10 #HT10 #H destruct
@@ -120,7 +131,7 @@ lemma cprs_inv_abbr1: ∀a,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{a}V1.T1 ➡* U2 →
   ]
 | #U1 #HTU1 #HU01 elim (lift_total U2 0 1)
   #U #HU2 lapply (cpr_lift … HU02 (L.ⓓV1) … HU01 … HU2) -U0
-  /4 width=3 by cprs_strap1, ldrop_drop, ex3_intro, or_intror/
+  /4 width=3 by cprs_strap1, drop_drop, ex3_intro, or_intror/
 ]
 qed-.