initial properies of the "same top term constructor" predicate

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / unfold / tpss.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss.ma
index f21f3603eb01e5a35bd6d93460b2374f746bc7eb..16a0d3e4d9fb9a39e6b673c6e3704040a9cc3029 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss.ma
@@ -25,72 +25,72 @@ interpretation "partial unfold (term)"
 (* Basic eliminators ********************************************************)
 
 lemma tpss_ind: ∀d,e,L,T1. ∀R:predicate term. R T1 →
-                (â\88\80T,T2. L â\8a¢ T1 [d, e] â\89«* T â\86\92 L â\8a¢ T [d, e] â\89« T2 → R T → R T2) →
-                â\88\80T2. L â\8a¢ T1 [d, e] â\89«* T2 → R T2.
+                (â\88\80T,T2. L â\8a¢ T1 [d, e] â\96¶* T â\86\92 L â\8a¢ T [d, e] â\96¶ T2 → R T → R T2) →
+                â\88\80T2. L â\8a¢ T1 [d, e] â\96¶* T2 → R T2.
 #d #e #L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) //
 qed-.
 
 (* Basic properties *********************************************************)
 
 lemma tpss_strap: ∀L,T1,T,T2,d,e. 
-                  L â\8a¢ T1 [d, e] â\89« T â\86\92 L â\8a¢ T [d, e] â\89«* T2 â\86\92 L â\8a¢ T1 [d, e] â\89«* T2. 
-/2/ qed.
+                  L â\8a¢ T1 [d, e] â\96¶ T â\86\92 L â\8a¢ T [d, e] â\96¶* T2 â\86\92 L â\8a¢ T1 [d, e] â\96¶* T2. 
+/2 width=3/ qed.
 
-lemma tpss_lsubs_conf: â\88\80L1,T1,T2,d,e. L1 â\8a¢ T1 [d, e] â\89«* T2 →
-                       â\88\80L2. L1 [d, e] â\89¼ L2 â\86\92 L2 â\8a¢ T1 [d, e] â\89«* T2.
-/3/ qed.
+lemma tpss_lsubs_conf: â\88\80L1,T1,T2,d,e. L1 â\8a¢ T1 [d, e] â\96¶* T2 →
+                       â\88\80L2. L1 [d, e] â\89¼ L2 â\86\92 L2 â\8a¢ T1 [d, e] â\96¶* T2.
+/3 width=3/ qed.
 
-lemma tpss_refl: â\88\80d,e,L,T. L â\8a¢ T [d, e] â\89«* T.
-/2/ qed.
+lemma tpss_refl: â\88\80d,e,L,T. L â\8a¢ T [d, e] â\96¶* T.
+/2 width=1/ qed.
 
-lemma tpss_bind: â\88\80L,V1,V2,d,e. L â\8a¢ V1 [d, e] â\89«* V2 →
-                 ∀I,T1,T2. L. 𝕓{I} V2 ⊢ T1 [d + 1, e] ≫* T2 →
-                 L ⊢ 𝕓{I} V1. T1 [d, e] ≫* 𝕓{I} V2. T2.
-#L #V1 #V2 #d #e #HV12 elim HV12 -HV12 V2
-[ #V2 #HV12 #I #T1 #T2 #HT12 elim HT12 -HT12 T2
+lemma tpss_bind: â\88\80L,V1,V2,d,e. L â\8a¢ V1 [d, e] â\96¶* V2 →
+                 ∀I,T1,T2. L. ⓑ{I} V2 ⊢ T1 [d + 1, e] ▶* T2 →
+                 L ⊢ ⓑ{I} V1. T1 [d, e] ▶* ⓑ{I} V2. T2.
+#L #V1 #V2 #d #e #HV12 elim HV12 -V2
+[ #V2 #HV12 #I #T1 #T2 #HT12 elim HT12 -T2
   [ /3 width=5/
   | #T #T2 #_ #HT2 #IHT @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
   ]
 | #V #V2 #_ #HV12 #IHV #I #T1 #T2 #HT12
-  lapply (tpss_lsubs_conf … HT12 (L. 𝕓{I} V) ?) -HT12 /2/ #HT12
-  lapply (IHV … HT12) -IHV HT12 #HT12 @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
+  lapply (tpss_lsubs_conf … HT12 (L. ⓑ{I} V) ?) -HT12 /2 width=1/ #HT12
+  lapply (IHV … HT12) -IHV -HT12 #HT12 @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
 ]
 qed.
 
 lemma tpss_flat: ∀L,I,V1,V2,T1,T2,d,e.
-                 L â\8a¢ V1 [d, e] â\89« * V2 â\86\92 L â\8a¢ T1 [d, e] â\89«* T2 →
-                 L ⊢ 𝕗{I} V1. T1 [d, e] ≫* 𝕗{I} V2. T2.
-#L #I #V1 #V2 #T1 #T2 #d #e #HV12 elim HV12 -HV12 V2
-[ #V2 #HV12 #HT12 elim HT12 -HT12 T2
-  [ /3/
+                 L â\8a¢ V1 [d, e] â\96¶ * V2 â\86\92 L â\8a¢ T1 [d, e] â\96¶* T2 →
+                 L ⊢ ⓕ{I} V1. T1 [d, e] ▶* ⓕ{I} V2. T2.
+#L #I #V1 #V2 #T1 #T2 #d #e #HV12 elim HV12 -V2
+[ #V2 #HV12 #HT12 elim HT12 -T2
+  [ /3 width=1/
   | #T #T2 #_ #HT2 #IHT @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
   ]
 | #V #V2 #_ #HV12 #IHV #HT12
-  lapply (IHV … HT12) -IHV HT12 #HT12 @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
+  lapply (IHV … HT12) -IHV -HT12 #HT12 @step /2 width=5/ (**) (* /3 width=5/ is too slow *)
 ]
 qed.
 
-lemma tpss_weak: â\88\80L,T1,T2,d1,e1. L â\8a¢ T1 [d1, e1] â\89«* T2 →
+lemma tpss_weak: â\88\80L,T1,T2,d1,e1. L â\8a¢ T1 [d1, e1] â\96¶* T2 →
                  ∀d2,e2. d2 ≤ d1 → d1 + e1 ≤ d2 + e2 →
-                 L â\8a¢ T1 [d2, e2] â\89«* T2.
-#L #T1 #T2 #d1 #e1 #H #d1 #d2 #Hd21 #Hde12 @(tpss_ind … H) -H T2
+                 L â\8a¢ T1 [d2, e2] â\96¶* T2.
+#L #T1 #T2 #d1 #e1 #H #d1 #d2 #Hd21 #Hde12 @(tpss_ind … H) -T2
 [ //
 | #T #T2 #_ #HT12 #IHT
-  lapply (tps_weak … HT12 … Hd21 Hde12) -HT12 Hd21 Hde12 /2/
+  lapply (tps_weak … HT12 … Hd21 Hde12) -HT12 -Hd21 -Hde12 /2 width=3/
 ]
 qed.
 
 lemma tpss_weak_top: ∀L,T1,T2,d,e.
-                     L â\8a¢ T1 [d, e] â\89«* T2 â\86\92 L â\8a¢ T1 [d, |L| - d] â\89«* T2.
-#L #T1 #T2 #d #e #H @(tpss_ind … H) -H T2
+                     L â\8a¢ T1 [d, e] â\96¶* T2 â\86\92 L â\8a¢ T1 [d, |L| - d] â\96¶* T2.
+#L #T1 #T2 #d #e #H @(tpss_ind … H) -T2
 [ //
 | #T #T2 #_ #HT12 #IHT
-  lapply (tps_weak_top … HT12) -HT12 /2/
+  lapply (tps_weak_top … HT12) -HT12 /2 width=3/
 ]
 qed.
 
 lemma tpss_weak_all: ∀L,T1,T2,d,e.
-                     L â\8a¢ T1 [d, e] â\89«* T2 â\86\92 L â\8a¢ T1 [0, |L|] â\89«* T2.
+                     L â\8a¢ T1 [d, e] â\96¶* T2 â\86\92 L â\8a¢ T1 [0, |L|] â\96¶* T2.
 #L #T1 #T2 #d #e #HT12
 lapply (tpss_weak … HT12 0 (d + e) ? ?) -HT12 // #HT12
 lapply (tpss_weak_top … HT12) //
@@ -99,38 +99,47 @@ qed.
 (* Basic inversion lemmas ***************************************************)
 
 (* Note: this can be derived from tpss_inv_atom1 *)
-lemma tpss_inv_sort1: â\88\80L,T2,k,d,e. L â\8a¢ â\8b\86k [d, e] â\89«* T2 → T2 = ⋆k.
-#L #T2 #k #d #e #H @(tpss_ind … H) -H T2
+lemma tpss_inv_sort1: â\88\80L,T2,k,d,e. L â\8a¢ â\8b\86k [d, e] â\96¶* T2 → T2 = ⋆k.
+#L #T2 #k #d #e #H @(tpss_ind … H) -T2
 [ //
-| #T #T2 #_ #HT2 #IHT destruct -T
+| #T #T2 #_ #HT2 #IHT destruct
   >(tps_inv_sort1 … HT2) -HT2 //
 ]
 qed-.
 
-lemma tpss_inv_bind1: ∀d,e,L,I,V1,T1,U2. L ⊢ 𝕓{I} V1. T1 [d, e] ≫* U2 →
-                      ∃∃V2,T2. L ⊢ V1 [d, e] ≫* V2 & 
-                               L. 𝕓{I} V2 ⊢ T1 [d + 1, e] ≫* T2 &
-                               U2 =  𝕓{I} V2. T2.
-#d #e #L #I #V1 #T1 #U2 #H @(tpss_ind … H) -H U2
+(* Note: this can be derived from tpss_inv_atom1 *)
+lemma tpss_inv_gref1: ∀L,T2,p,d,e. L ⊢ §p [d, e] ▶* T2 → T2 = §p.
+#L #T2 #p #d #e #H @(tpss_ind … H) -T2
+[ //
+| #T #T2 #_ #HT2 #IHT destruct
+  >(tps_inv_gref1 … HT2) -HT2 //
+]
+qed-.
+
+lemma tpss_inv_bind1: ∀d,e,L,I,V1,T1,U2. L ⊢ ⓑ{I} V1. T1 [d, e] ▶* U2 →
+                      ∃∃V2,T2. L ⊢ V1 [d, e] ▶* V2 & 
+                               L. ⓑ{I} V2 ⊢ T1 [d + 1, e] ▶* T2 &
+                               U2 =  ⓑ{I} V2. T2.
+#d #e #L #I #V1 #T1 #U2 #H @(tpss_ind … H) -U2
 [ /2 width=5/
-| #U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct -U;
+| #U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct
   elim (tps_inv_bind1 … HU2) -HU2 #V2 #T2 #HV2 #HT2 #H
-  lapply (tpss_lsubs_conf … HT1 (L. 𝕓{I} V2) ?) -HT1 /3 width=5/
+  lapply (tpss_lsubs_conf … HT1 (L. ⓑ{I} V2) ?) -HT1 /2 width=1/ /3 width=5/
 ]
 qed-.
 
-lemma tpss_inv_flat1: ∀d,e,L,I,V1,T1,U2. L ⊢ 𝕗{I} V1. T1 [d, e] ≫* U2 →
-                      â\88\83â\88\83V2,T2. L â\8a¢ V1 [d, e] â\89«* V2 & L â\8a¢ T1 [d, e] â\89«* T2 &
-                               U2 =  𝕗{I} V2. T2.
-#d #e #L #I #V1 #T1 #U2 #H @(tpss_ind … H) -H U2
+lemma tpss_inv_flat1: ∀d,e,L,I,V1,T1,U2. L ⊢ ⓕ{I} V1. T1 [d, e] ▶* U2 →
+                      â\88\83â\88\83V2,T2. L â\8a¢ V1 [d, e] â\96¶* V2 & L â\8a¢ T1 [d, e] â\96¶* T2 &
+                               U2 =  ⓕ{I} V2. T2.
+#d #e #L #I #V1 #T1 #U2 #H @(tpss_ind … H) -U2
 [ /2 width=5/
-| #U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct -U;
+| #U #U2 #_ #HU2 * #V #T #HV1 #HT1 #H destruct
   elim (tps_inv_flat1 … HU2) -HU2 /3 width=5/
 ]
 qed-.
 
-lemma tpss_inv_refl_O2: â\88\80L,T1,T2,d. L â\8a¢ T1 [d, 0] â\89«* T2 → T1 = T2.
-#L #T1 #T2 #d #H @(tpss_ind … H) -H T2
+lemma tpss_inv_refl_O2: â\88\80L,T1,T2,d. L â\8a¢ T1 [d, 0] â\96¶* T2 → T1 = T2.
+#L #T1 #T2 #d #H @(tpss_ind … H) -T2
 [ //
 | #T #T2 #_ #HT2 #IHT <(tps_inv_refl_O2 … HT2) -HT2 //
 ]