update in ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cprs_cprs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_cprs.ma
index 76e2da87ea1685961d9dbdb8a2747ba9b89350ef..fe6b36fcd2ef2edb7be9cac9ee64e9547db062cf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_cprs.ma
@@ -12,10 +12,10 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/reduction/lpr_lpr.ma".
-include "basic_2/computation/cprs_lift.ma".
+include "basic_2/rt_transition/lpr_lpr.ma".
+include "basic_2/rt_computation/cpms_cpms.ma".
 
-(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
+(* CONTEXT-SENSITIVE PARALLEL COMPUTATION FOR TERMS *************************)
 
 (* Main properties **********************************************************)
 
@@ -29,47 +29,15 @@ normalize /2 width=3 by trans_TC/ qed-.
 theorem cprs_conf: ∀G,L. confluent2 … (cprs G L) (cprs G L).
 normalize /3 width=3 by cpr_conf, TC_confluent2/ qed-.
 
-theorem cprs_bind: ∀a,I,G,L,V1,V2,T1,T2. ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ V1 ➡* V2 →
-                   ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡* ⓑ{a,I}V2.T2.
-#a #I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cprs_ind … H) -V2
-/3 width=5 by cprs_trans, cprs_bind_dx/
-qed.
-
 (* Basic_1: was: pr3_flat *)
-theorem cprs_flat: ∀I,G,L,V1,V2,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ V1 ➡* V2 →
-                   ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ➡* ⓕ{I}V2.T2.
-#I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cprs_ind … H) -V2
-/3 width=3 by cprs_flat_dx, cprs_strap1, cpr_pair_sn/
-qed.
-
-theorem cprs_beta_rc: ∀a,G,L,V1,V2,W1,W2,T1,T2.
-                      ⦃G, L⦄ ⊢ V1 ➡ V2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ W1 ➡* W2 →
-                      ⦃G, L⦄ ⊢ ⓐV1.ⓛ{a}W1.T1 ➡* ⓓ{a}ⓝW2.V2.T2.
-#a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HT12 #H @(cprs_ind … H) -W2 /2 width=1 by cprs_beta_dx/
-#W #W2 #_ #HW2 #IHW1 (**) (* fulla uto too slow 14s *)
-@(cprs_trans … IHW1) -IHW1 /3 width=1 by cprs_flat_dx, cprs_bind/
-qed.
-
-theorem cprs_beta: ∀a,G,L,V1,V2,W1,W2,T1,T2.
-                   ⦃G, L.ⓛW1⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ W1 ➡* W2 → ⦃G, L⦄ ⊢ V1 ➡* V2 →
-                   ⦃G, L⦄ ⊢ ⓐV1.ⓛ{a}W1.T1 ➡* ⓓ{a}ⓝW2.V2.T2.
-#a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HT12 #HW12 #H @(cprs_ind … H) -V2 /2 width=1 by cprs_beta_rc/
-#V #V2 #_ #HV2 #IHV1
-@(cprs_trans … IHV1) -IHV1 /3 width=1 by cprs_flat_sn, cprs_bind/
-qed.
-
-theorem cprs_theta_rc: ∀a,G,L,V1,V,V2,W1,W2,T1,T2.
-                       ⦃G, L⦄ ⊢ V1 ➡ V → ⬆[0, 1] V ≘ V2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ➡* T2 →
-                       ⦃G, L⦄ ⊢ W1 ➡* W2 → ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡* ⓓ{a}W2.ⓐV2.T2.
-#a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 #HT12 #H @(cprs_ind … H) -W2
-/3 width=5 by cprs_trans, cprs_theta_dx, cprs_bind_dx/
-qed.
-
-theorem cprs_theta: ∀a,G,L,V1,V,V2,W1,W2,T1,T2.
-                    ⬆[0, 1] V ≘ V2 → ⦃G, L⦄ ⊢ W1 ➡* W2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ➡* T2 →
-                    ⦃G, L⦄ ⊢ V1 ➡* V → ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡* ⓓ{a}W2.ⓐV2.T2.
-#a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV2 #HW12 #HT12 #H @(cprs_ind_dx … H) -V1
-/3 width=3 by cprs_trans, cprs_theta_rc, cprs_flat_dx/
+theorem cprs_flat (h) (G) (L):
+                  ∀T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h] T2 →
+                  ∀V1,V2. ⦃G, L⦄ ⊢ V1 ➡*[h] V2 →
+                  ∀I. ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ➡*[h] ⓕ{I}V2.T2.
+#h #G #L #T1 #T2 #HT12 #V1 #V2 #H @(cprs_ind_dx … H) -V2
+[ /2 width=3 by cprs_flat_dx/
+| /3 width=3 by cpr_pair_sn, cprs_step_dx/
+]
 qed.
 
 (* Advanced inversion lemmas ************************************************)
@@ -100,34 +68,6 @@ lemma cprs_inv_appl1: ∀G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡* U2 →
 ]
 qed-.
 
-(* Properties concerning sn parallel reduction on local environments ********)
-
-(* Basic_1: was just: pr3_pr2_pr2_t *)
-(* Basic_1: includes: pr3_pr0_pr2_t *)
-lemma lpr_cpr_trans: ∀G. b_c_transitive … (cpr G) (λ_. lpr G).
-#G #L2 #T1 #T2 #HT12 elim HT12 -G -L2 -T1 -T2
-[ /2 width=3 by/
-| #G #L2 #K2 #V0 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV02 #L1 #HL12
-  elim (lpr_drop_trans_O1 … HL12 … HLK2) -L2 #X #HLK1 #H
-  elim (lpr_inv_pair2 … H) -H #K1 #V1 #HK12 #HV10 #H destruct
-  /4 width=6 by cprs_strap2, cprs_delta/
-|3,7: /4 width=1 by lpr_pair, cprs_bind, cprs_beta/
-|4,6: /3 width=1 by cprs_flat, cprs_eps/
-|5,8: /4 width=3 by lpr_pair, cprs_zeta, cprs_theta, cprs_strap1/
-]
-qed-.
-
-lemma cpr_bind2: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡ V2 → ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡ T2 →
-                 ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡* ⓑ{a,I}V2.T2.
-/4 width=5 by lpr_cpr_trans, cprs_bind_dx, lpr_pair/ qed.
-
-(* Advanced properties ******************************************************)
-
-(* Basic_1: was only: pr3_pr2_pr3_t pr3_wcpr0_t *)
-lemma lpr_cprs_trans: ∀G. b_rs_transitive … (cpr G) (λ_. lpr G).
-#G @b_c_trans_CTC1 /2 width=3 by lpr_cpr_trans/ (**) (* full auto fails *)
-qed-.
-
 (* Basic_1: was: pr3_strip *)
 (* Basic_1: includes: pr1_strip *)
 lemma cprs_strip: ∀G,L. confluent2 … (cprs G L) (cpr G L).
@@ -148,8 +88,3 @@ lemma cprs_lpr_conf_sn: ∀G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ➡* T1 →
 #G #L0 #T0 #T1 #HT01 #L1 #HL01 elim (cprs_lpr_conf_dx … HT01 … HL01) -HT01
 /3 width=3 by lpr_cprs_trans, ex2_intro/
 qed-.
-
-lemma cprs_bind2_dx: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡ V2 →
-                     ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡* T2 →
-                     ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡* ⓑ{a,I}V2.T2.
-/4 width=5 by lpr_cprs_trans, cprs_bind_dx, lpr_pair/ qed.