severe bug found in parallel zeta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpm_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma
index 4f04adc8fd0d073fb298f011a9e21f0972914cf0..beddc2697d0e9a5277ec643012c1a8048be7cc6a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma
@@ -17,6 +17,34 @@ include "basic_2/rt_transition/cpm.ma".
 
 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
 
+(* Properties with generic slicing for local environments *******************)
+
+(* Basic_1: includes: pr0_lift pr2_lift *)
+(* Basic_2A1: includes: cpr_lift *)
+lemma cpm_lifts_sn: ∀n,h,G. d_liftable2_sn … lifts (λL. cpm h G L n).
+#n #h #G #K #T1 #T2 * #c #Hc #HT12 #b #f #L #HLK #U1 #HTU1
+elim (cpg_lifts_sn … HT12 … HLK … HTU1) -K -T1
+/3 width=5 by ex2_intro/
+qed-.
+
+lemma cpm_lifts_bi: ∀n,h,G. d_liftable2_bi … lifts (λL. cpm h G L n).
+#n #h #G #K #T1 #T2 * /3 width=11 by cpg_lifts_bi, ex2_intro/
+qed-.
+
+(* Inversion lemmas with generic slicing for local environments *************)
+
+(* Basic_1: includes: pr0_gen_lift pr2_gen_lift *)
+(* Basic_2A1: includes: cpr_inv_lift1 *)
+lemma cpm_inv_lifts_sn: ∀n,h,G. d_deliftable2_sn … lifts (λL. cpm h G L n).
+#n #h #G #L #U1 #U2 * #c #Hc #HU12 #b #f #K #HLK #T1 #HTU1
+elim (cpg_inv_lifts_sn … HU12 … HLK … HTU1) -L -U1
+/3 width=5 by ex2_intro/
+qed-.
+
+lemma cpm_inv_lifts_bi: ∀n,h,G. d_deliftable2_bi … lifts (λL. cpm h G L n).
+#n #h #G #L #U1 #U2 * /3 width=11 by cpg_inv_lifts_bi, ex2_intro/
+qed-.
+
 (* Advanced properties ******************************************************)
 
 (* Basic_1: includes: pr2_delta1 *)
@@ -74,30 +102,69 @@ lemma cpm_inv_lref1_drops: ∀n,h,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡[n, h] T2 →
 ]
 qed-.
 
-(* Properties with generic slicing for local environments *******************)
-
-(* Basic_1: includes: pr0_lift pr2_lift *)
-(* Basic_2A1: includes: cpr_lift *)
-lemma cpm_lifts_sn: ∀n,h,G. d_liftable2_sn … lifts (cpm n h G).
-#n #h #G #K #T1 #T2 * #c #Hc #HT12 #b #f #L #HLK #U1 #HTU1
-elim (cpg_lifts_sn … HT12 … HLK … HTU1) -K -T1
-/3 width=5 by ex2_intro/
-qed-.
-
-lemma cpm_lifts_bi: ∀n,h,G. d_liftable2_bi … lifts (cpm n h G).
-#n #h #G #K #T1 #T2 * /3 width=11 by cpg_lifts_bi, ex2_intro/
-qed-.
-
-(* Inversion lemmas with generic slicing for local environments *************)
+(* Advanced forward lemmas **************************************************)
 
-(* Basic_1: includes: pr0_gen_lift pr2_gen_lift *)
-(* Basic_2A1: includes: cpr_inv_lift1 *)
-lemma cpm_inv_lifts_sn: ∀n,h,G. d_deliftable2_sn … lifts (cpm n h G).
-#n #h #G #L #U1 #U2 * #c #Hc #HU12 #b #f #K #HLK #T1 #HTU1
-elim (cpg_inv_lifts_sn … HU12 … HLK … HTU1) -L -U1
-/3 width=5 by ex2_intro/
+fact cpm_fwd_plus_aux (n) (h): ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 →
+                               ∀n1,n2. n1+n2 = n →
+                               ∃∃T. ⦃G, L⦄ ⊢ T1 ➡[n1, h] T & ⦃G, L⦄ ⊢ T ➡[n2, h] T2.
+#n #h #G #L #T1 #T2 #H @(cpm_ind … H) -G -L -T1 -T2 -n
+[ #I #G #L #n1 #n2 #H
+  elim (plus_inv_O3 … H) -H #H1 #H2 destruct
+  /2 width=3 by ex2_intro/
+| #G #L #s #x1 #n2 #H
+  elim (plus_inv_S3_sn … H) -H *
+  [ #H1 #H2 destruct /2 width=3 by ex2_intro/
+  | #n1 #H1 #H elim (plus_inv_O3 … H) -H #H2 #H3 destruct
+    /2 width=3 by ex2_intro/
+  ]
+| #n #G #K #V1 #V2 #W2 #_ #IH #HVW2 #n1 #n2 #H destruct
+  elim IH [|*: // ] -IH #V #HV1 #HV2
+  elim (lifts_total V 𝐔❴↑O❵) #W #HVW
+  /5 width=11 by cpm_lifts_bi, cpm_delta, drops_refl, drops_drop, ex2_intro/
+| #n #G #K #V1 #V2 #W2 #HV12 #IH #HVW2 #x1 #n2 #H
+  elim (plus_inv_S3_sn … H) -H *
+  [ #H1 #H2 destruct -IH /3 width=3 by cpm_ell, ex2_intro/
+  | #n1 #H1 #H2 destruct -HV12
+    elim (IH n1) [|*: // ] -IH #V #HV1 #HV2
+    elim (lifts_total V 𝐔❴↑O❵) #W #HVW
+    /5 width=11 by cpm_lifts_bi, cpm_ell, drops_refl, drops_drop, ex2_intro/
+  ]
+| #n #I #G #K #T2 #U2 #i #_ #IH #HTU2 #n1 #n2 #H destruct
+  elim IH [|*: // ] -IH #T #HT1 #HT2
+  elim (lifts_total T 𝐔❴↑O❵) #U #HTU
+  /5 width=11 by cpm_lifts_bi, cpm_lref, drops_refl, drops_drop, ex2_intro/
+| #n #p #I #G #L #V1 #V2 #T1 #T2 #HV12 #_ #_ #IHT #n1 #n2 #H destruct
+  elim IHT [|*: // ] -IHT #T #HT1 #HT2
+  /3 width=5 by cpm_bind, ex2_intro/
+| #n #G #L #V1 #V2 #T1 #T2 #HV12 #_ #_ #IHT #n1 #n2 #H destruct
+  elim IHT [|*: // ] -IHT #T #HT1 #HT2
+  /3 width=5 by cpm_appl, ex2_intro/
+| #n #G #L #U1 #U2 #T1 #T2 #_ #_ #IHU #IHT #n1 #n2 #H destruct
+  elim IHU [|*: // ] -IHU #U #HU1 #HU2
+  elim IHT [|*: // ] -IHT #T #HT1 #HT2
+  /3 width=5 by cpm_cast, ex2_intro/
+| #n #G #K #V #U1 #T1 #T2 #HTU1 #_ #IH #n1 #n2 #H destruct
+  elim IH [|*: // ] -IH #T #HT1 #HT2
+  /3 width=3 by cpm_zeta, ex2_intro/
+| #n #G #L #U #T1 #T2 #_ #IH #n1 #n2 #H destruct
+  elim IH [|*: // ] -IH #T #HT1 #HT2
+  /3 width=3 by cpm_eps, ex2_intro/
+| #n #G #L #U1 #U2 #T #HU12 #IH #x1 #n2 #H
+  elim (plus_inv_S3_sn … H) -H *
+  [ #H1 #H2 destruct -IH /3 width=4 by cpm_ee, cpm_cast, ex2_intro/
+  | #n1 #H1 #H2 destruct -HU12
+    elim (IH n1) [|*: // ] -IH #U #HU1 #HU2
+    /3 width=3 by cpm_ee, ex2_intro/
+  ]
+| #n #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #_ #_ #_ #IH #n1 #n2 #H destruct
+  elim IH [|*: // ] -IH #T #HT1 #HT2
+  /4 width=7 by cpm_beta, cpm_appl, cpm_bind, ex2_intro/
+| #n #p #G #L #V1 #V2 #U2 #W1 #W2 #T1 #T2 #HV12 #HW12 #_ #_ #_ #IH #HVU2 #n1 #n2 #H destruct
+  elim IH [|*: // ] -IH #T #HT1 #HT2
+  /4 width=7 by cpm_theta, cpm_appl, cpm_bind, ex2_intro/
+]
 qed-.
 
-lemma cpm_inv_lifts_bi: ∀n,h,G. d_deliftable2_bi … lifts (cpm n h G).
-#n #h #G #L #U1 #U2 * /3 width=11 by cpg_inv_lifts_bi, ex2_intro/
-qed-.
+lemma cpm_fwd_plus (h) (G) (L): ∀n1,n2,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n1+n2, h] T2 →
+                                ∃∃T. ⦃G, L⦄ ⊢ T1 ➡[n1, h] T & ⦃G, L⦄ ⊢ T ➡[n2, h] T2.
+/2 width=3 by cpm_fwd_plus_aux/ qed-.