- first properties of strongly normalizing terms

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

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss.ma
index eb7803efe9631f72c282720ea9076685596aef24..207bfc60f3059526eb80e0140d6887e47748a201 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss.ma
@@ -25,83 +25,91 @@ interpretation "partial unfold (local environment)"
 
 (* Basic eliminators ********************************************************)
 
-lemma ltpss_ind: ∀d,e,L1. ∀R: lenv → Prop. R L1 →
-                 (â\88\80L,L2. L1 [d, e] â\89«* L â\86\92 L [d, e] â\89« L2 → R L → R L2) →
-                 â\88\80L2. L1 [d, e] â\89«* L2 → R L2.
+lemma ltpss_ind: ∀d,e,L1. ∀R:predicate lenv. R L1 →
+                 (â\88\80L,L2. L1 [d, e] â\96¶* L â\86\92 L [d, e] â\96¶ L2 → R L → R L2) →
+                 â\88\80L2. L1 [d, e] â\96¶* L2 → R L2.
 #d #e #L1 #R #HL1 #IHL1 #L2 #HL12 @(TC_star_ind … HL1 IHL1 … HL12) //
-qed.
+qed-.
 
 (* Basic properties *********************************************************)
 
 lemma ltpss_strap: ∀L1,L,L2,d,e.
-                   L1 [d, e] ≫ L → L [d, e] ≫* L2 → L1 [d, e] ≫* L2. 
-/2/ qed.
+                   L1 [d, e] ▶ L → L [d, e] ▶* L2 → L1 [d, e] ▶* L2. 
+/2 width=3/ qed.
+
+lemma ltpss_refl: ∀L,d,e. L [d, e] ▶* L.
+/2 width=1/ qed.
+
+lemma ltpss_weak_all: ∀L1,L2,d,e. L1 [d, e] ▶* L2 → L1 [0, |L2|] ▶* L2.
+#L1 #L2 #d #e #H @(ltpss_ind … H) -L2 //
+#L #L2 #_ #HL2
+>(ltps_fwd_length … HL2) /3 width=5/
+qed.
 
-lemma ltpss_refl: ∀L,d,e. L [d, e] ≫* L.
-/2/ qed.
+(* Basic forward lemmas *****************************************************)
+
+lemma ltpss_fwd_length: ∀L1,L2,d,e. L1 [d, e] ▶* L2 → |L1| = |L2|.
+#L1 #L2 #d #e #H @(ltpss_ind … H) -L2 //
+#L #L2 #_ #HL2 #IHL12 >IHL12 -IHL12
+/2 width=3 by ltps_fwd_length/
+qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma ltpss_inv_refl_O2: â\88\80d,L1,L2. L1 [d, 0] â\89«* L2 → L1 = L2.
+lemma ltpss_inv_refl_O2: â\88\80d,L1,L2. L1 [d, 0] â\96¶* L2 → L1 = L2.
 #d #L1 #L2 #H @(ltpss_ind … H) -L2 //
 #L #L2 #_ #HL2 #IHL <(ltps_inv_refl_O2 … HL2) -HL2 //
-qed.
+qed-.
 
-lemma ltpss_inv_atom1: â\88\80d,e,L2. â\8b\86 [d, e] â\89«* L2 → L2 = ⋆.
+lemma ltpss_inv_atom1: â\88\80d,e,L2. â\8b\86 [d, e] â\96¶* L2 → L2 = ⋆.
 #d #e #L2 #H @(ltpss_ind … H) -L2 //
-#L #L2 #_ #HL2 #IHL destruct -L
+#L #L2 #_ #HL2 #IHL destruct
 >(ltps_inv_atom1 … HL2) -HL2 //
-qed.
-(*
-fact ltps_inv_atom2_aux: ∀d,e,L1,L2.
-                         L1 [d, e] ≫ L2 → L2 = ⋆ → L1 = ⋆.
-#d #e #L1 #L2 * -d e L1 L2
-[ //
-| #L #I #V #H destruct
-| #L1 #L2 #I #V1 #V2 #e #_ #_ #H destruct
-| #L1 #L2 #I #V1 #V2 #d #e #_ #_ #H destruct
-]
-qed.
+qed-.
 
-lemma ldrop_inv_atom2: ∀d,e,L1. L1 [d, e] ≫ ⋆ → L1 = ⋆.
-/2 width=5/ qed.
+fact ltpss_inv_atom2_aux: ∀d,e,L1,L2. L1 [d, e] ▶* L2 → L2 = ⋆ → L1 = ⋆.
+#d #e #L1 #L2 #H @(ltpss_ind … H) -L2 //
+#L2 #L #_ #HL2 #IHL2 #H destruct
+lapply (ltps_inv_atom2 … HL2) -HL2 /2 width=1/
+qed.
 
-fact ltps_inv_tps22_aux: ∀d,e,L1,L2. L1 [d, e] ≫ L2 → d = 0 → 0 < e →
-                         ∀K2,I,V2. L2 = K2. 𝕓{I} V2 →
-                         ∃∃K1,V1. K1 [0, e - 1] ≫ K2 &
-                                  K2 ⊢ V1 [0, e - 1] ≫ V2 &
-                                  L1 = K1. 𝕓{I} V1.
+lemma ltpss_inv_atom2: ∀d,e,L1. L1 [d, e] ▶* ⋆ → L1 = ⋆.
+/2 width=5/ qed-.
+(*
+fact ltps_inv_tps22_aux: ∀d,e,L1,L2. L1 [d, e] ▶ L2 → d = 0 → 0 < e →
+                         ∀K2,I,V2. L2 = K2. ⓑ{I} V2 →
+                         ∃∃K1,V1. K1 [0, e - 1] ▶ K2 &
+                                  K2 ⊢ V1 [0, e - 1] ▶ V2 &
+                                  L1 = K1. ⓑ{I} V1.
 #d #e #L1 #L2 * -d e L1 L2
 [ #d #e #_ #_ #K1 #I #V1 #H destruct
 | #L1 #I #V #_ #H elim (lt_refl_false … H)
-| #L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #_ #_ #K2 #J #W2 #H destruct -L2 I V2 /2 width=5/
+| #L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #_ #_ #K2 #J #W2 #H destruct /2 width=5/
 | #L1 #L2 #I #V1 #V2 #d #e #_ #_ #H elim (plus_S_eq_O_false … H)
 ]
 qed.
 
-lemma ltps_inv_tps22: â\88\80e,L1,K2,I,V2. L1 [0, e] â\89« K2. ð\9d\95\93{I} V2 → 0 < e →
-                      â\88\83â\88\83K1,V1. K1 [0, e - 1] â\89« K2 & K2 â\8a¢ V1 [0, e - 1] â\89« V2 &
-                               L1 = K1. 𝕓{I} V1.
+lemma ltps_inv_tps22: â\88\80e,L1,K2,I,V2. L1 [0, e] â\96¶ K2. â\93\91{I} V2 → 0 < e →
+                      â\88\83â\88\83K1,V1. K1 [0, e - 1] â\96¶ K2 & K2 â\8a¢ V1 [0, e - 1] â\96¶ V2 &
+                               L1 = K1. ⓑ{I} V1.
 /2 width=5/ qed.
 
-fact ltps_inv_tps12_aux: â\88\80d,e,L1,L2. L1 [d, e] â\89« L2 → 0 < d →
-                         ∀I,K2,V2. L2 = K2. 𝕓{I} V2 →
-                         â\88\83â\88\83K1,V1. K1 [d - 1, e] â\89« K2 &
-                                  K2 â\8a¢ V1 [d - 1, e] â\89« V2 &
-                                  L1 = K1. 𝕓{I} V1.
+fact ltps_inv_tps12_aux: â\88\80d,e,L1,L2. L1 [d, e] â\96¶ L2 → 0 < d →
+                         ∀I,K2,V2. L2 = K2. ⓑ{I} V2 →
+                         â\88\83â\88\83K1,V1. K1 [d - 1, e] â\96¶ K2 &
+                                  K2 â\8a¢ V1 [d - 1, e] â\96¶ V2 &
+                                  L1 = K1. ⓑ{I} V1.
 #d #e #L1 #L2 * -d e L1 L2
 [ #d #e #_ #I #K2 #V2 #H destruct
 | #L #I #V #H elim (lt_refl_false … H)
 | #L1 #L2 #I #V1 #V2 #e #_ #_ #H elim (lt_refl_false … H)
-| #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #_ #J #K2 #W2 #H destruct -L2 I V2
-  /2 width=5/
+| #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #_ #J #K2 #W2 #H destruct /2 width=5/
 ]
 qed.
 
-lemma ltps_inv_tps12: ∀L1,K2,I,V2,d,e. L1 [d, e] ≫ K2. 𝕓{I} V2 → 0 < d →
-                      ∃∃K1,V1. K1 [d - 1, e] ≫ K2 &
-                                  K2 ⊢ V1 [d - 1, e] ≫ V2 &
-                                  L1 = K1. 𝕓{I} V1.
-/2/ qed.
-
+lemma ltps_inv_tps12: ∀L1,K2,I,V2,d,e. L1 [d, e] ▶ K2. ⓑ{I} V2 → 0 < d →
+                      ∃∃K1,V1. K1 [d - 1, e] ▶ K2 &
+                                  K2 ⊢ V1 [d - 1, e] ▶ V2 &
+                                  L1 = K1. ⓑ{I} V1.
+/2 width=1/ qed.
 *)