more results on strongly normalizing terms

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / computation / csn_lift.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/computation/csn_lift.ma b/matita/matita/contribs/lambda_delta/Basic_2/computation/csn_lift.ma
index 605e78db110f0c89e344cc58e84e3c12eed9d386..2e816b72c30feedcf9ebfb6f4840ed580a137bb4 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/computation/csn_lift.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/computation/csn_lift.ma
@@ -18,6 +18,29 @@ include "Basic_2/computation/csn.ma".
 
 (* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERMS *****************************)
 
+(* Relocation properties ****************************************************)
+
+(* Basic_1: was: sn3_lift *)
+lemma csn_lift: ∀L2,L1,T1,d,e. L1 ⊢ ⬇* T1 →
+                ∀T2. ⇩[d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → L2 ⊢ ⬇* T2.
+#L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL21 #HT12
+@csn_intro #T #HLT2 #HT2
+elim (cpr_inv_lift … HL21 … HT12 … HLT2) -HLT2 #T0 #HT0 #HLT10
+@(IHT1 … HLT10) // -L1 -L2 #H destruct
+>(lift_mono … HT0 … HT12) in HT2; -T0 /2 width=1/
+qed.
+
+(* Basic_1: was: sn3_gen_lift *)
+lemma csn_inv_lift: ∀L2,L1,T1,d,e. L1 ⊢ ⬇* T1 →
+                    ∀T2. ⇩[d, e] L1 ≡ L2 → ⇧[d, e] T2 ≡ T1 → L2 ⊢ ⬇* T2.
+#L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21
+@csn_intro #T #HLT2 #HT2
+elim (lift_total T d e) #T0 #HT0
+lapply (cpr_lift … HL12 … HT21 … HT0 HLT2) -HLT2 #HLT10
+@(IHT1 … HLT10) // -L1 -L2 #H destruct
+>(lift_inj … HT0 … HT21) in HT2; -T0 /2 width=1/
+qed.
+
 (* Advanced properties ******************************************************)
 
 lemma csn_acp: acp cpr (eq …) (csn …).
@@ -29,6 +52,21 @@ lemma csn_acp: acp cpr (eq …) (csn …).
 ]
 qed.
 
+(* Basic_1: was: sn3_abbr *)
+lemma csn_lref_abbr: ∀L,K,V,i. ⇩[0, i] L ≡ K. ⓓV → K ⊢ ⬇* V → L ⊢ ⬇* #i.
+#L #K #V #i #HLK #HV
+@csn_intro #X #H #Hi
+elim (cpr_inv_lref1 … H) -H
+[ #H destruct elim (Hi ?) //
+| -Hi * #K0 #V0 #V1 #HLK0 #HV01 #HV1 #_
+  lapply (ldrop_mono … HLK0 … HLK) -HLK #H destruct
+  lapply (ldrop_fwd_ldrop2 … HLK0) -HLK0 #HLK
+  @(csn_lift … HLK HV1) -HLK -HV1
+  @(csn_cpr_trans … HV) -HV
+  @(cpr_intro … HV01) -HV01 //
+]
+qed.
+
 lemma csn_abst: ∀L,W. L ⊢ ⬇* W → ∀I,V,T. L. ⓑ{I} V ⊢ ⬇* T → L ⊢ ⬇* ⓛW. T.
 #L #W #HW elim HW -W #W #_ #IHW #I #V #T #HT @(csn_ind … HT) -T #T #HT #IHT
 @csn_intro #X #H1 #H2
@@ -39,26 +77,24 @@ elim (eq_false_inv_tpair … H2) -H2
 | -HLW0 * #H destruct /3 width=1/
 ]
 qed.
+(*
+axiom eq_false_inv_tpair_dx: ∀I,V1,T1,V2,T2.
+                             (②{I} V1. T1 = ②{I} V2. T2 → False) →
+                             (T1 = T2 → False) ∨ (T1 = T2 ∧ (V1 = V2 → False)).
+                             
+#I #V1 #T1 #V2 #T2 #H
+elim (term_eq_dec V1 V2) /3 width=1/ #HV12 destruct
+@or_intror @conj // #HT12 destruct /2 width=1/ 
+qed-.
 
-(* Relocation properties ****************************************************)
-
-(* Basic_1: was: sn3_lift *)
-lemma csn_lift: ∀L2,L1,T1,d,e. L1 ⊢ ⬇* T1 →
-                ∀T2. ⇩[d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → L2 ⊢ ⬇* T2.
-#L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL21 #HT12
-@csn_intro #T #HLT2 #HT2
-elim (cpr_inv_lift … HL21 … HT12 … HLT2) -HLT2 #T0 #HT0 #HLT10
-@(IHT1 … HLT10) // -L1 -L2 #H destruct
->(lift_mono … HT0 … HT12) in HT2; -T0 /2 width=1/
-qed.
-
-(* Basic_1: was: sn3_gen_lift *)
-lemma csn_inv_lift: ∀L2,L1,T1,d,e. L1 ⊢ ⬇* T1 →
-                    ∀T2. ⇩[d, e] L1 ≡ L2 → ⇧[d, e] T2 ≡ T1 → L2 ⊢ ⬇* T2.
-#L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21
-@csn_intro #T #HLT2 #HT2
-elim (lift_total T d e) #T0 #HT0
-lapply (cpr_lift … HL12 … HT21 … HT0 HLT2) -HLT2 #HLT10
-@(IHT1 … HLT10) // -L1 -L2 #H destruct
->(lift_inj … HT0 … HT21) in HT2; -T0 /2 width=1/
+lemma csn_appl_simple: ∀L,T. L ⊢ ⬇* T → 𝐒[T] → ∀V. L ⊢ ⬇* V → L ⊢ ⬇* ⓐV. T.
+#L #T #H elim H -T #T #_ #IHT #HT #V #H @(csn_ind … H) -V #V #HV #IHV 
+@csn_intro #X #H1 #H2
+elim (cpr_inv_appl1_simple … H1 ?) // -H1
+#V0 #T0 #HLV0 #HLT0 #H destruct
+elim (eq_false_inv_tpair_dx … H2) -H2
+[ -IHV #HT0 @IHT -IHT // -HLT0 /2 width=1/ -HT0 /2 width=3/   
+| -HV -HT -IHT -HLT0 * #H #HV0 destruct /3 width=1/
+]
 qed.
+*)
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