commit by user andrea

[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..1326a8bb482d556adf75daa324d495250180b580 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
@@ -18,28 +18,6 @@ include "Basic_2/computation/csn.ma".
 
 (* CONTEXT-SENSITIVE STRONGLY NORMALIZING TERMS *****************************)
 
-(* Advanced properties ******************************************************)
-
-lemma csn_acp: acp cpr (eq …) (csn …).
-@mk_acp
-[ /2 width=1/
-| /2 width=3/
-| /2 width=5/
-| @cnf_lift
-]
-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
-elim (cpr_inv_abst1 … H1 I V) -H1
-#W0 #T0 #HLW0 #HLT0 #H destruct
-elim (eq_false_inv_tpair … H2) -H2
-[ /3 width=5/
-| -HLW0 * #H destruct /3 width=1/
-]
-qed.
-
 (* Relocation properties ****************************************************)
 
 (* Basic_1: was: sn3_lift *)
@@ -62,3 +40,59 @@ 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 …).
+@mk_acp
+[ /2 width=1/
+| /2 width=3/
+| /2 width=5/
+| @cnf_lift
+]
+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
+elim (cpr_inv_abst1 … H1 I V) -H1
+#W0 #T0 #HLW0 #HLT0 #H destruct
+elim (eq_false_inv_tpair_sn … H2) -H2
+[ /3 width=5/
+| -HLW0 * #H destruct /3 width=1/
+]
+qed.
+
+lemma csn_appl_simple: ∀L,V. L ⊢ ⬇* V → ∀T1.
+                       (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → False) → L ⊢ ⬇* ⓐV. T2) →
+                       𝐒[T1] → L ⊢ ⬇* ⓐV. T1.
+#L #V #H @(csn_ind … H) -V #V #_ #IHV #T1 #IHT1 #HT1
+@csn_intro #X #H1 #H2
+elim (cpr_inv_appl1_simple … H1 ?) // -H1
+#V0 #T0 #HLV0 #HLT10 #H destruct
+elim (eq_false_inv_tpair_dx … H2) -H2
+[ -IHV -HT1 #HT10
+  @(csn_cpr_trans … (ⓐV.T0)) /2 width=1/ -HLV0
+  @IHT1 -IHT1 // /2 width=1/
+| -HLT10 * #H #HV0 destruct
+  @IHV -IHV // -HT1 /2 width=1/ -HV0
+  #T2 #HLT02 #HT02
+  @(csn_cpr_trans … (ⓐV.T2)) /2 width=1/ -HLV0
+  @IHT1 -IHT1 // -HLT02 /2 width=1/
+]
+qed.